Question

this graph shows how the total number of stamps zach has in his collection is related to the amount of money he spends on additional stamps.
stamps in zach’s collection
how much money does zach need to spend on new stamps in order to have a total of 50 stamps in his collection?
$90 $100 $30 $70

Explanation:

Step1: Identify initial stamp count

When \$0 is spent, total stamps = 10.

Step2: Calculate stamps to gain

Total desired stamps = 50. Stamps needed: $50 - 10 = 40$

Step3: Find rate of stamps per dollar

From graph: \$100 spent gives 50 total stamps. Stamps gained: $50 - 10 = 40$ for \$100. Rate: $\frac{40 \text{ stamps}}{\$100} = 0.4 \text{ stamps per dollar}$

Step4: Calculate required spending

Money needed: $\frac{40 \text{ stamps}}{0.4 \text{ stamps per dollar}} = \$100$
Alternatively, directly read from the graph: the line reaches 50 stamps at \$100 spent.

Answer:

\$100