Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. ben and his cousin beth are picking apples in their grandparents orchard. ben has filled 5 baskets with apples and is filling them at a rate of 5 baskets per hour. beth has 14 full baskets and will continue picking at 2 baskets per hour. once the cousins get to the point where they have the same number of baskets, they will carry them to the barn and then eat lunch. how much fruit will they have picked by then? how long will that take? ben and beth will each have filled baskets in hours.

Explanation:

Step1: Define variables

Let \( t = \) time in hours, \( B = \) Ben's baskets, \( H = \) Beth's baskets.

Step2: Write equations

Ben: \( B = 5 + 2t \)
Beth: \( H = 14 + 5t \)
Set equal: \( 5 + 2t = 14 + 5t \)

Step3: Solve for \( t \)

\( 2t - 5t = 14 - 5 \)
\( -3t = 9 \)
\( t = -3 \)

Step4: Check validity

Negative time is impossible; they never have same baskets.

Answer:

They will never have the same number of filled baskets (negative time result means no solution).
Ben and Beth will each have filled -1 baskets in -3 hours (invalid, so no real solution).