Money, payment and change

Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.

1. What you will learn

2. Starting point

Add equal prices and subtract amounts of the same currency. Payment handed over and price paid need not be equal before change is returned.

3. Words for this lesson

4. Payment need not be another wanted good

Imagine a person with spare pencils wants a notebook. Exchanging pencils directly for the notebook would require the notebook provider to accept the pencils under agreed terms. A direct exchange of goods or services is called barter. Such an exchange can work, but it depends on finding an arrangement that both sides accept. We should not assume that every provider wants whatever the buyer happens to offer.

Money makes many exchanges easier because people widely accept it as payment. A notebook provider may accept dollars even when they do not want pencils. They can later use those dollars for a different accepted payment. Money acts as a medium of exchange: something used between receiving income or other funds and obtaining goods or services.

This is a description of one function of money, not a claim that all societies followed one simple history from barter to coins. People have organized exchange, gifts, debts and payment in many ways. Our classroom cases use a stated currency and a provider who accepts it. The calculation follows that arrangement rather than pretending that every possible exchange works identically.

Acceptance has boundaries. A voucher for one activity may not be accepted at another place. A shop in one country may not accept another country's notes. Later lessons explain currencies and exchange rates. Here, every price and payment is in the same named currency, dollars, so we can focus on the amounts without mixing different units.

Term	What it means
Money	Something widely accepted for payment and used as a common unit of account.
Barter	Direct exchange of goods or services.
Price	The amount required for the specified purchase.
Denomination	The amount a note or coin represents.
Change	Payment above the price returned to the payer.
Balance	The amount recorded or held at a stated time.

Another way: Count value, not just pieces

Different pieces of money can represent different amounts. A one-dollar coin and a two-dollar coin are two pieces, but together they represent three dollars. Counting pieces alone would not tell us whether there is enough value to pay a three-dollar price. Read the denomination, which is the amount each note or coin represents in the exercise.

For example, one five-dollar note and two one-dollar coins make seven dollars. Five plus one plus one equals seven. There are three physical pieces, but seven dollars of value. Keep those counts separate. A problem asking how many pieces are present has a different answer from a problem asking how many dollars they represent.

Money need not be only notes and coins. In many payment arrangements, people use balances recorded in accounts and transfer part of a balance electronically. The screen or card helps arrange the payment; it is not an unlimited source of money. If a case gives an account balance, a payment must be accounted for against that balance under the stated rules.

For our calculations, the available amount is always supplied. Do not add imagined borrowing or an unspecified gift to make a purchase possible. If seven dollars are available and an item costs nine dollars, the stated funds are two dollars short. That is a comparison of available money and price, not a judgment about whether the person deserves the item.

Another way: A price is an amount per stated purchase

A price tells us the money required for the specified purchase. If a notebook costs three dollars each, two notebooks cost six dollars under a rule with no additional charge or discount. Three plus three equals six. The word each matters: a three-dollar price for a pack of two notebooks would describe a different arrangement.

Read what the quoted price includes. Does it describe one product, a bundle, a session, or a period of time? A four-dollar entry price is not automatically four dollars for every minute inside. A two-dollar pack of cards is not automatically two dollars for each card. Before multiplying, identify the unit attached to the price.

In this course, purchase cases state the full price to be paid. We do not invent a tax, fee, delivery charge or discount when none is supplied. Later courses teach how those additions work when they are given. The present task is to use the stated complete amount consistently.

Prices let people express different purchases in a common unit. A five-dollar book and a three-dollar pen together cost eight dollars under the stated conditions. This comparison does not mean that a book's importance can be reduced to its price, or that every person prefers it to the pen. Price is payment information. Preferences, available resources and the purpose of the purchase are additional parts of a choice.

Another way: Follow payment and change in both directions

Suppose a purchase costs seven dollars and the customer hands over a ten-dollar note. The note's value exceeds the price by three dollars. Under the stated cash-payment arrangement, the provider gives three dollars in change. Ten dollars go to the provider first; three dollars return to the customer. The provider keeps seven dollars, matching the price.

Change is not a discount or a new gift. It returns the part of the payment that exceeds the agreed price. A useful check is price plus change equals the amount handed over. Seven plus three equals ten. If a proposed answer gives four dollars of change, seven plus four equals eleven, which does not match the ten-dollar payment.

The customer's money falls by the price, not by the price plus the amount handed over. If the customer starts with fifteen dollars, hands over ten and receives three back, the ending amount is eight dollars. Fifteen minus ten plus three equals eight. The shorter calculation, fifteen minus the seven-dollar price, also gives eight. Both methods follow the same transaction.

Do not count the returned change twice. Adding the change to the shorter price-subtraction calculation would produce the wrong balance. Use either the complete cash flow or the net price change, then check that they agree. Following both routes is a good way to understand why the remaining money has its value.

Another way: Money measures a balance, not every resource

Having enough money for a price does not prove that every part of a plan is feasible. A person may have the stated entry price for two events that happen at the same time, yet be unable to attend both. A money calculation checks one resource constraint. The time condition must still be checked separately.

Likewise, a larger money balance does not describe all a person's resources or all their well-being. A household may have useful possessions, skills, relationships and access to shared services. Some of those can help meet needs even though they are not money. We should not call every useful resource money just because it matters economically.

Money can also carry purchasing ability from one time to another. Setting some aside today can help pay for a later purchase. But a number of dollars is not a guarantee that every future price will stay the same. A price can change. The saving lesson first uses an explicitly unchanged price, and later economics lessons examine changing prices.

The boundary matters for a careful answer. If an exercise asks how much remains after a purchase, calculate the balance from the stated transaction. Do not turn that result into a claim that the person is wealthy, happy, or able to afford every future expense. The answer describes a particular amount under supplied conditions.

Another way: Check a whole transaction record

A short record can contain the starting money, the full purchase price, the amount handed over, the change, and the ending money. Not every question needs every column, but recording them helps distinguish quantities that are easy to confuse. The amount handed over can be greater than the price; the net reduction in the customer's money equals the price in this simple case.

Suppose a customer has fourteen dollars and buys two three-dollar notebooks. The total price is six dollars. Paying with a ten-dollar note gives four dollars in change. The ending balance is eight dollars. Check the purchase first: three plus three equals six. Check change next: six plus four equals ten. Check the wallet last: fourteen minus ten plus four equals eight.

A payment smaller than the price does not generate negative change. If the price is six dollars and only four are handed over, two dollars remain unpaid under the stated arrangement. Report the missing payment. Do not describe it as change owed to the customer. The direction of the difference depends on which amount is larger.

A receipt provides another check: compare its listed item quantities and full prices with the actual goods received. An arithmetic total can be correct for the wrong number of items, so verify the description as well as the addition.

Finally, keep every amount in the same currency and use its name. Eight dollars is clear; eight with no unit may mean products, coins or minutes elsewhere in a problem. A complete explanation connects the arithmetic to who gives and receives money. That is more useful than memorizing a subtraction rule without knowing what its quantities represent.

5. A library craft stall's transaction record

A fictional library craft stall lists small notebooks at three dollars each, with all charges included. A visitor has fourteen dollars and chooses two notebooks. The visitor pays using a ten-dollar note. The stall accepts dollars and can provide the required change. These stated conditions make the transaction fully specified.

Calculate the purchase price first. Two notebooks at three dollars each cost six dollars. The ten-dollar payment is four dollars above the price, so the stall returns four dollars. Check that six dollars retained by the stall plus four dollars returned to the visitor equals the ten dollars initially handed over.

Now check the visitor's remaining money. Fourteen dollars at the start, minus ten handed over, plus four returned gives eight dollars. Subtracting the six-dollar total price from the original fourteen also gives eight. The two routes agree. Adding four dollars of change again after subtracting the price would count the returned money twice.

The two notebooks flow from the stall to the visitor. The net money payment flows from the visitor to the stall. Drawing those directions separately prevents a product-flow arrow from being mistaken for a payment arrow. This record checks the transaction arithmetic; it does not recommend a purchase, judge the price, or assume that a fictional notebook price applies at any real shop. It also says nothing about the visitor's other future needs. The answer is the balance and exchange described in this particular case.

6. A tempting mistake

Do not count notes instead of their dollar value. Do not subtract both price and payment from the starting balance; payment minus returned change already equals the price.

7. Different pieces, one total value

8. A payment larger than the price

9. Two products and the ending wallet

10. A nine-dollar purchase paid with twelve dollars

11. Guided practice

A visitor starts with 14 dollars, buys two notebooks at 3 dollars each, and hands over 10 dollars. All charges are included. Give the total price, returned change and ending money, all in dollars.

12. Guided practice

A visitor has seventeen dollars, buys two three-dollar items, and hands over ten dollars. Complete the transaction.

13. Guided practice

At a stall S, customer C hands over a 5-dollar payment and receives a notebook. In this diagram draw only the direct supply of the notebook, not the payment flow.

14. Practice

A buyer starts with 18 dollars, buys three cards at 2 dollars each, and pays with 10 dollars. All charges are included. Give the total price, returned change and ending money, all in dollars.

15. Practice

A buyer starts with 20 dollars, buys two kits at 4 dollars each, and hands over exactly 8 dollars. All charges are included. Give the total price, returned change and ending money, all in dollars.

16. Somewhere new

At a fictional community event, a visitor has 17 dollars, buys three programs at 3 dollars each, and hands over 12 dollars. All charges are included. Give the total price, returned change and ending money, all in dollars.

17. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

18. Test question

A buyer starts with 16 dollars, buys two packs at 5 dollars each, and hands over 15 dollars. All charges are included. Give the total price, returned change and ending money, all in dollars.

19. What you can do now

Explain how to trace an accepted money payment and check price, change and remaining money. Show a fresh example and check its result.

	Your result
Total price in dollars
Change in dollars
Ending dollars

	Your result
Total price in dollars
Change in dollars
Ending dollars

	Your result
Total price in dollars
Change in dollars
Ending dollars