Maths Olympiad Prep

Library / /104 of 168

Algebra Difficulty 2.0 Junior Find the answer

Seven students shared the cost of a $26.00\$26.00 pizza. Each student paid either $3.71\$3.71 or $3.72\$3.72. How many students paid $3.72\$3.72?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

We can rephrase the given information by saying that each of the seven students paid $3.71\$3.71 and some of the students paid an extra $0.01\$0.01. Since 7×$3.71=$25.977 \times \$3.71=\$25.97 and the pizza cost $26.00\$26.00 in total, then the students who paid the extra $0.01\$0.01 each must make up the final $0.03\$0.03 of the cost of the pizza. Therefore, 3 students each paid an additional $0.01\$0.01 and so paid $3.72\$3.72 in total.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.