Question

Isabella is buying art supplies. The table shows the prices for the different items she buys.

Art Supplies
Item Price
Glass beads $0.28 per ounce
Paint brush $0.95
Poster board $0.75
Jar of paint $0.99

Part 1
Isabella spends $4.50 on poster boards. How many poster boards does she buy?

Isabella buys poster boards.

Part 2 out of 2
Isabella spends $7.80 on paint brushes and paint. How many of each item does she buy? Complete the explanation how you found your answer.

By using compatible numbers, you find a total of items that had a total cost of $7.80. Then you used guess and check to find that she buys paint brushes and jars of paint.

Answer 1

1. 6 poster boards
2. 3 paint brushes, 5 jars of paint

Explanation:

Given poster boards are $0.75 each, you want to know the number purchased for $4.50. Given brushes are $0.95 and jars of paint are $0.99, you want to know the number of each purchased for $7.80.

1.

The total price is the quantity times the price each:

4.50 = q × 0.75

q = 4.50/0.75 = 6

Isabella buys 6 poster boards.

2.

Compatible numbers for the costs of brushes and paint are each 1. A compatible number for the total purchase is 8. This tells us Isabella bought 8 items for 7.80. This gives two equations in two unknowns:

0.95b +0.99p = 7.80

b + p = 8

Substituting for b, we have ...

0.95(8 -p) +0.99p = 7.80

`7.60 +0.04p = 7.80 . . . . . . simplify

0.04p = 0.20 . . . . . . . . . . . subtract 7.60

p = 0.20/0.04 = 5

b = 8 -5 = 3

Isabella buys 3 paint brushes and 5 jars of paint.

Check

0.95(3) +0.99(5) = 2.85 +4.95 = 7.80 . . . . answer checks OK

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Additional comment

Note that we do not need to "guess and check" once we know the number of items purchased.

Or, we can "guess" without the business of compatible numbers by realizing the number of jars must be a multiple of 5 if the total purchase is a multiple of 5 cents. That leaves one possibility, since 10 jars is too many, and 0 jars is not enough.