Problem

Largest vertical gap between two line graphs

One line graph shows Mia's and Liam's weights at ages 7, 8, 9, 10, 11. Mia: 24, 26, 27, 32, 30 kg; Liam: 20, 22, 25, 26, 27 kg (each small square = 1 kg). I must find the age where the two weights are closest and give that smallest difference.

Measurement & data

Your answer

How to solve

Strategy Make a Systematic List — There are only five ages, so I list the vertical gap (Mia minus Liam) at each age and pick the smallest. Looking at the graph, the smallest gap is where the two lines come closest together vertically.

1STEP 1

Find the gap at each age

Subtract Liam's weight from Mia's at each age: age7: 24-20=4, age8: 26-22=4, age9: 27-25=2, age10: 32-26=6, age11: 30-27=3.

4, 4, 2, 6, 3

2STEP 2

Pick the smallest gap

Among 4, 4, 2, 6, 3 the smallest is 2, at age 9 — the two lines are just two squares apart there.

min(4,4,2,6,3) = 2 at age 9

Answer

At age 9, difference = 2 kg

At age 9 Mia is 27 and Liam is 25, a 2 kg gap, and every other age gives 3 kg or more, so age 9 is correctly the closest. Each square is 1 kg, and the lines there are 2 squares apart, matching the answer.

Takeaway

The two lines are closest where their gap is smallest - just check each point and pick the tiniest difference!

Find the gap at each age
Pick the smallest gap

Where next?

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