Question

Tommy, Ali, and Jack each have a band. Tommy’s band has won three less awards then Ali. Jacks band has won twice as many bands as Tommy. They have a total of 23 awards. Find the number of awards each persons’ band has won.

Answer 1

Answer: Tommy won 5 awards. Ali won 8 awards. Jack won 10 awards.

Explanation:

First give each person a variable:

Tommy = y

Ali = a

Jack = x

Then figure out the equations:

Tommy won 3 less awards than Ali, so the equation would be (y = a - 3).

Jack won twice as many awards as Tommy, so the equation would be (x = 2y)

All three won a total of 23, so that would be (23 = y + x + a)

Next, plug in (2y) into the (x) of (23 = y + x + a)

This would result in (23 = 3y + a)

Then you would plug in (a - 3) into (y)

This would result in (23 = 4a - 9)

Solve for a: (a = 8)

Now that you know (a = 8), plug that into the first equation (y = a - 3) to find (y).

Answer: (y = 5)

Use (y = 5) and plug it into the second equation (x = 2y) to find (x)

Answer: (x = 10)

Answers:

a = 8

y = 5

x = 10

Answer 2

Tommy's band won 5 awards, Ali's band won 8 awards and Jack's band won 10 awards.

Explanation:

Let the number of awards Tommy won be x.

Number of awards Ali won -> x+3

Number of awards Jack won -> 2x

`x+x+3+2x=23`

`4x+3=23`

Subtract 3 from both sides:

`4x+3-3=23-3`

`4x=20`

Divide both sides by 4:

`(4x)/(4)=(20)/(4)`

`x=5` (Tommy)

`5+3=8` (Ali)

`5*2=10` (Jack)