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

Ball cost 5 cents

Add 1 dollar

That is $1.05

Add that to the cost of the ball

Total is $1.10

What is 1.05 + .05? 1.10. If the ball was .10, the bat would be 1.10, bringing the total to 1.20

Because if it were 10, the bat would cost 1$. Which means the bat is 90 cents more than the ball. Bat – 1.05. Ball – 0.05. Total – 1.10. 1.05-0.05=1$. Hope this helped.

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The bat doesn’t cost $1, it cost $1 MORE than the ball. If the ball cost 10 cents, the bat would cost $ 1.10 for a total of $1.20. The ball cost 5 cents making the bat $1.05 for a total of $1.10.

If the original cost of the ball is 5 cents then 0.05+(1+0.05)=1.10.

It’s the only way this could work, if the ball was 10 cents then it would be 0.10+(1+0.10)=$1.20.

So: x = price of the bat , y = price of the ball, x+y=1.10 but also x=y+1.00.. so substituting x you have y + 1.00 + y = 1.10 meaning 2y = 0.10, thus y = 0.05.

Bat + Ball = 1.10 (1)

Bat = 1 + Ball (2)

Substitute (2) in (1)

(1 + Ball) + Ball = 1.10

1 + 2Ball = 1.10

2 Ball = 1.10 – 1

2Ball = 0.10

Ball = 0.10 / 2

Therefore, Ball = 0.05 (3)

Substitute (3) in (1) to find cost of Bat.

Bat + 0.05 = 1.10

Hence, Bat = 1.10 – 0.05 = 1.05

Bat (1.05) costs 1 dollar more than the Ball (0.05).

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Simple: `$0.05 + $1.05 = $1.10` if it was 10 cent instead it would not work out `$0.10 + $1.10 ≠ $1.10` This is not exactly college level math.

I think your mistake is here to confuse the total with the price of the bat. The total is the price of the ball and the bat. If the ball was ten cent and the bat was one dollar more then the bat would be one dollar and ten cent and the total would one dollar and twenty cent.

To do it the math way you do it in school. 🦇 is the bat and ⚾ is the ball.

🦇 + ⚾ = $1.10

and

🦇 = ⚾ + $1.00

Put the second equation in the first and you get

⚾ + $1.00 + ⚾ = $1.10

move stuff around a bit and you get:

⚾ + ⚾ + $1.00 = $1.10

subtrract $1 from both sides and you get

⚾ + ⚾ = $0.10

divide both sides by two and you get

⚾ = $0.05

put that into the first equation and you get

🦇 + $0.05 = $1.10

subtract $0.04 from both sides and you get

🦇 = $1.05

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.

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.