Question

Question #839d2

Answer 1

`9" peaches and " 3" grapefruit"`

Explanation:

`"4parts "to" 12 pears"`

`rArr"1 part "to12/4=color(red)(3)`

`rArr"peaches "=3xxcolor(red)(3)=9`

`rArr"grapefruit "=1xxcolor(red)(3)=3`

Answer 2

Calculate one part of the ratio and then mutiply.

Explanation:

1. Calculate what one part of the ratio equals. 4 parts equals 12 so therefore 1 part would equal 3.

2. Peaches : Grapefruit : Pears
   3 :1 :4
   We know what one part equals so we can substitute in.
   (3×3) :(1×3) :(4×3)
   9 :3 :12

Looking at this we can see there are 9 peaches and 3 grapefruits.

Hope this has helped.

Answer 3

There are `9` peaches and `3` grapefruit.

Explanation:

In this case we have the simplified ratio of

`"peaches : grapefruit : pears"`
`" "3color(white)(xxx):color(white)(xxx)1color(white)(xxx):color(white)(xxx)4`

But we want to know the actual numbers of the fruit.
There are 12 pears.

`4 xx 3 =12`

`"peaches : grapefruit : pears"`

`" "3color(white)(xxx):color(white)(xxx)1color(white)(xxx):color(white)(xxxx)4`
`" "darrcolor(white)(xx)color(white)(xxx)darrcolor(white)(xxx):color(white)(xxx)darr`
`" "color(white)(xxxxxxxxxxxxxxx)xx3" "larr (4xx3 =12)`
`" "darrcolor(white)(xx)color(white)(xxx)darrcolor(white)(xxx):color(white)(xxx)darr`
`" "?color(white)(xxx):color(white)(xxx)?color(white)(xxx):color(white)(xxx)12`

so now multiply the other parts of the ratio by `3` as well.

`" "3color(white)(xxx):color(white)(xxx)1color(white)(xxx):color(white)(xxxx)4`
`" "darrcolor(white)(xx)color(white)(xxx)darrcolor(white)(xxx):color(white)(xxx)darr`

`" "xx3color(white)(xxxx)xx3color(white)(xxxxx)xx3`
`" "darrcolor(white)(xx)color(white)(xxx)darrcolor(white)(xxx):color(white)(xxx)darr`

`" "9color(white)(xxx):color(white)(xxx)3color(white)(xxx):color(white)(xxxx)12`

There are `9` peaches and `3` grapefruit.

Answer 4

There are `9` peaches and `3` grapefruit in the basket along with the `12` pears.

Explanation:

We have a fixed ratio of peaches, to grapefruit, to pears as `3:1:4`.

It looks like: `pe3:gr1:pr4`

We are also given that there is a quantity of `12` pears which we have represented above by `pr4`.

Then to find the quantity of each fruit we need to multiply the entire ratio by `cancel((pr)12)/cancel((pr)4)=3`

The quantity of each fruit is then: `3xx(pe3:gr1:pr4)`

`=pe9+gr3+pr12`

Now we need some apples.