Question

Dave has 3 times as many sweets as Will. Debbie has 3 sweets less than Dave. Together, they have 53 sweets. What is the simplest ratio between the number of sweets that Will has to the number that Dave has to the number that Debbie has?

Answer 1

The simplest ratio between the number of sweets that Will has to the number that Dave has to the number that Debbie has is `8:24:21`.

Explanation:

Let the number of sweets,

Will have be `x`,
Dave have be `y`, and,
Debbie have be `z` respectively.

`y=3xrarr①`
`z=y-3rarr②`
`x+y+z=53rarr③`

Substitute `①` into `②`,

`z=3x-3rarr④`

Substitute `①` and `④` into `③`,

`x+(3x)+(3x-3)=53`
`color(white)(" ")7x=56`
`color(white)(" ")x=8`

When `x=8`,

`y=3(8)`
`color(white)(y)=24`

`z=3(8)-3`
`color(white)(z)=21`

Hence, Will has `8` candies, Dave has `24` candies and Debbie has `21` candies.

Will`:`Dave`:`Debbie
`color(white)(" ")8:color(white)(" ")24:color(white)(" ")21`

Answer 2

Will : Dave : Debbie

`=8:24:21`

Explanation:

First we need to fond out how many they each have,

Will has the fewest sweets. Let that number be `x`

Dave has `3` times as many: That is `3x`
Debbie has `3` less than Dave. That is `3x-3`

Together they have `53`

`x+3x+3x-3=53`

`7x-3=53`

`7x =56`

`x=8`

Will have `8`, Dave has `24` and Debbie has `21`

Will : Dave : Debbie

`=8:24:21`

This does not simplify