Question

resent the situation and then solve. be sure to define your
in katys garden there are 105 ladybugs. they are
increasing at two ladybugs per month. there are currently
175 aphids and the number of aphids is decreasing at
three aphids per month. when will the number of ladybugs
and aphids in katys garden be the same?

Explanation:

Step1: Define variables

Let $x$ = number of months from now, $L(x)$ = number of ladybugs, $A(x)$ = number of aphids.

Step2: Write ladybug population formula

Ladybugs start at 105, increase by 2/month:
$L(x) = 105 + 2x$

Step3: Write aphid population formula

Aphids start at 175, decrease by 3/month:
$A(x) = 175 - 3x$

Step4: Set populations equal

Find $x$ where $L(x)=A(x)$:
$105 + 2x = 175 - 3x$

Step5: Solve for x

Add $3x$ to both sides:
$105 + 5x = 175$
Subtract 105 from both sides:
$5x = 70$
Divide by 5:
$x = \frac{70}{5} = 14$

Answer:

14 months