Work through 2026 AMC 8 Problem 7 on fractions and proportions with a written solution, hints, and a visual explanation.
AlgebraLevel 2 · Core skill
Mika would like to estimate how far she can ride a new model of electric bike on a fully charged battery. She completed two trips totaling 40 miles. The first trip used 1/2 of the total battery power, while the second trip used 3/10 of the total battery power. How many miles can this electric bike go on a fully charged battery?
A. 45
B. 48
C. 50
D. 52
E. 55
Hints
Add the two battery fractions used on the two trips.
Give both fractions a common denominator so you can combine them into one fraction of the full battery.
If that combined fraction of the battery equals 40 miles, divide to find what a full (100%) battery equals.
Read the step-by-step solution
Answer: C · 50 miles
Find total battery used
Total battery used = 1/2 + 3/10 = 5/10 + 3/10 = 8/10 = 4/5.
1/2 + 3/10 = 4/5
Find full range
40 miles used 4/5 of the battery, so full range = 40 ÷ (4/5) = 40 × 5/4 = 50 miles.