Question

Joseph and Wendy were catching tadpoles. At first Wendy caught nine times three more than Joseph caught. Joseph was upset and released half of Wendy ’s tadpoles, and then six times as many as Joseph caught swam away. After all of this, Wendy only had three tadpoles left. How many tadpoles did Joseph catch?

Answer 1

7

Explanation:

Step 1: translate the given word problem into solvable algebraic equation.

Let "t" represent the number of tadpoles Joseph caught.

"Wendy caught nine times three more than Joseph caught" can be expressed as 9(t + 3)

Number of Wendy's tadpole =
`9(t + 3)`

Given that half of Wendy's tadpole and also 6 times Joseph's tadpoles swarm away leaving Wendy with only 3, the following equation can be written:

`(9(t + 3))/(2) - 6t = 3`

Step 2: solve for t using the equation created.

`(9(t + 3))/(2) - 6t = 3`

Add 6t to both sides

`(9(t + 3))/(2) - 6t + 6t = 3 + 6t`

`(9(t + 3))/(2) = 3 + 6t`

Multiply both sides by 2

`(9(t + 3))/(2)*2 = (3 + 6t)*2`

`9(t + 3) = 2(3 + 6t)`

`9t + 27 = 6 + 12t`

Collect like terms

`9t - 12t = 6 - 27`

`-3t = -21`

Divide both sides by -3

`t = 7`

Joseph caught 7 tadpoles