Why is the answer to this question 5 cents and not 10 cents? “A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?”

Question

Why is the answer to this question 5 cents and not 10 cents? “A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?”

In: Mathematics

Answer 1

If the ball costs $0.10, then the bat would cost $1.10. In total, that would be $1.20 for the bat and ball.

If the ball costs $0.05, then the bat costs $1.05. Together, $1.10.

Answer 2

Premise 1:

bat + ball = 1.1

Premise 2:

bat = ball + 1

Therefore, from premise 2 we can alter premise 1:

ball + 1 + ball = 1.1

2ball + 1 = 1.1

2ball = 0.1

Result 1:

ball = 0.5

Splicing result 1 in to premise 1 :

bat + 0.5 = 1.1

Result 2:

bat = 1.05

The ball costs 5 cents, the bat one dollar and five cents.