Problem of the Month: April 2022

This month, we’re celebrating the start of baseball season by sharing the classic “Bat-and-Ball” problem! Even though the arithmetic is relatively simple, this puzzle is famous because people often get it wrong. Give it a try and scroll down to check out the solution!

A bat and a ball cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?

Did you come up with $0.10? Although $1 + $0.10 equals $1.10, $1 – $0.10 = $0.90. The problem requires that the bat costs $1 more than the ball.

Thus, the ball must cost $0.05, and the bat must cost $1.05 since $1.05 + $0.05 = $1.10.

You can solve using algebra.

Let x = the cost of the ball. We know the bat costs $1 more than the ball, so we can write the cost of the bat as (x + 1).

Thus, x + (1 + x) = 1.10

Rearranging and combining like terms, we have:  1  + 2x = 1.10

2x = 1.10 – 1

2x = 0.10

x = 0.05

Check our work, we plug in 0.05 for x:

x + (1 + x) = 1.10

0.05 + (1 + 0.05) = 1.10

The cost of the ball is $0.05 and the cost of the bat is $1.05.