Question

Your aunt lends you \(\$ 175\) to buy a guitar. She will decrease the amount you owe by \(\$ 25\) for each day you help her by doing odd jobs. Write a verbal model that you can use to find the decrease in the amount you owe your aunt depending on the number of days you help her out.

Short answer

The verbal model is: 'The amount owed is equal to $175 minus the product of the number of days worked and $25.'

Step-by-step solution

Define the Variables

Let's denote the total amount owed by the letter 'A' and the number of days the student works with the letter 'D'.

Establish the initial condition

Initially, the student owes $175 to the aunt, so we can write this as \( A = 175 \) when \( D = 0 \).

Establish the rate of decrease

Next, it is stated that for each day the student works, the amount owed decreases by $25. In other words, every increase in 'D' by 1 results in a decrease of 'A' by $25.

Write down the verbal model

The verbal model can thus be expressed as follows: The amount owed (A) is equal to $175 minus the product of the number of days worked (D) and 25.