Question

example 3
write and evaluate expressions
malik and two friends earn ( m ) dollars in one week doing odd jobs. they split the earnings so that each friend gets ( \frac{1}{3} ) of the total earnings. malik uses ( $22.50 ) of his earnings on lunch each week. last week, the three friends earned ( $963 ). how much money did malik have left after paying for lunch?
write an expression to represent how much malik has left. then evaluate the expression for the given value.
( \frac{1}{3}m - 32.5 )
( = \frac{1}{3}(963) - 32.5 )
( = 288.5 )
malik had ( $288.50 ) left after paying for lunch.

Explanation:

Step1: Identify Earnings and Split

Malik earns \( m \) dollars, and each friend gets \( \frac{1}{3} \) of total earnings. Total earnings for Malik and two friends: \( m + \frac{1}{3}m+\frac{1}{3}m=\frac{5}{3}m \)? Wait, no—wait, the problem says "they split the earnings so that each friend gets \( \frac{1}{3} \) of the total earnings". Wait, maybe total earnings is Malik's \( m \) plus friends? No, re-reading: "Malik and two friends earn \( m \) dollars in one week doing odd jobs. They split the earnings so that each friend gets \( \frac{1}{3} \) of the total earnings." Wait, total earnings is \( m \) (since Malik and two friends earn \( m \) together). So each friend gets \( \frac{1}{3}m \), two friends: \( 2\times\frac{1}{3}m=\frac{2}{3}m \). So Malik's earnings after splitting: \( m - \frac{2}{3}m=\frac{1}{3}m \). Then he uses \( \$32.50 \) on lunch each week. Last week, total earnings \( m = 963 \)? Wait, the example shows \( \frac{1}{3}(963)-32.5 \).

Step2: Substitute and Calculate

First, calculate \( \frac{1}{3} \) of 963: \( \frac{963}{3}=321 \). Then subtract 32.5: \( 321 - 32.5 = 288.5 \). Wait, the example says \( \frac{1}{3}(963)-32.5 = 321 - 32.5 = 288.5 \), and Malik had \( \$288.50 \) left. So the expression is \( \frac{1}{3}m - 32.5 \), and evaluating for \( m = 963 \) gives 288.5.

Answer:

The expression is \( \boldsymbol{\frac{1}{3}m - 32.5} \), and evaluating for \( m = 963 \) gives \( \boldsymbol{288.5} \) dollars left.