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B-47.

For each problem, write one or two equations to represent the situation and then solve. Be sure to define your variable(s) and clearly answer the question.

1. The Lee’s have three children. The oldest is twice as old as the youngest. The middle child is five years older than the youngest. If the sum of the ages is $57$, how old is each child?

Let $y =$ the youngest child.
Then, write an equation using the variable in which the sum of the children's ages equals $57$.

$y + (y + 5) + 2y = 57$
Solve for y then use it to find the age of each child.

1. In Katy’s 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 Katy’s garden be the same?

Let $x =$ months and let $y =$ insects.
Write two separate equations using $y = mx + b$, one for the ladybugs and one for the aphids.

$y = 2x + 105$
$y = 175 - 3x$

Use the Equal Values Method to solve for $x$.
$2x + 105 = 175 - 3x$