Question

homework 2.07

1. alexander was given a gift card for a coffee shop. each morning, alexander uses the card to buy one cup of coffee. each cup of coffee costs $1.50 and after buying 6 cups of coffee, the card had a $16 remaining balance.

a. write an equation for a, in terms of x, representing the amount of money remaining on the card after buying x cups of coffee.
b. how many cups of coffee did he buy if he had $10 remaining?

Explanation:

Step1: Find initial balance

First, find out how much was spent on 6 cups. Cost of 6 cups is $1.50\times6 = 9$. Since balance after 6 cups is $16$, initial balance $I=9 + 16=25$.

Step2: Write the equation

The amount of money $A$ remaining on the card after buying $x$ cups, with each cup costing $1.50$ and initial amount $25$ is $A = 25-1.5x$.

Step3: Solve for number of cups in part b

Set $A = 10$ in the equation $A = 25-1.5x$. So, $10=25 - 1.5x$. Rearrange to get $1.5x=25 - 10$. Then $1.5x = 15$. Solve for $x$: $x=\frac{15}{1.5}=10$.

Answer:

a. $A = 25-1.5x$
b. 10