Question

5-80. write an equation or system of equations to solve the problem below. apollo and zeus are both on diets. apollo currently weighs 105 kg and is gaining 2 kg per month. zeus currently weighs 130 kg and is losing 3 kg per month. in how many months will they weigh the same?

Explanation:

Step1: Define variables

Let $m$ = number of months, $A(m)$ = Apollo's weight, $Z(m)$ = Zeus's weight.

Step2: Apollo's weight equation

Apollo gains 2 kg/month starting from 105 kg:
$A(m) = 105 + 2m$

Step3: Zeus's weight equation

Zeus loses 3 kg/month starting from 130 kg:
$Z(m) = 130 - 3m$

Step4: Set weights equal

Set $A(m) = Z(m)$ to find when weights match:
$105 + 2m = 130 - 3m$

Step5: Solve for $m$

Add $3m$ to both sides:
$105 + 5m = 130$
Subtract 105 from both sides:
$5m = 25$
Divide by 5:
$m = \frac{25}{5} = 5$

Answer:

5 months