# Question 839d2

Jul 19, 2017

$9 \text{ peaches and " 3" grapefruit}$

#### Explanation:

$\text{4parts "to" 12 pears}$

$\Rightarrow \text{1 part } \to \frac{12}{4} = \textcolor{red}{3}$

$\Rightarrow \text{peaches } = 3 \times \textcolor{red}{3} = 9$

$\Rightarrow \text{grapefruit } = 1 \times \textcolor{red}{3} = 3$

Jul 19, 2017

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.

Jul 19, 2017

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

#### Explanation:

In this case we have the simplified ratio of

$\text{peaches : grapefruit : pears}$
$\text{ } 3 \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times x} 1 \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times x} 4$

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

$4 \times 3 = 12$

$\text{peaches : grapefruit : pears}$

$\text{ } 3 \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times x} 1 \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times \times} 4$
$\text{ } \downarrow \textcolor{w h i t e}{\times} \textcolor{w h i t e}{\times x} \downarrow \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times x} \downarrow$
$\text{ "color(white)(xxxxxxxxxxxxxxx)xx3" } \leftarrow \left(4 \times 3 = 12\right)$
$\text{ } \downarrow \textcolor{w h i t e}{\times} \textcolor{w h i t e}{\times x} \downarrow \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times x} \downarrow$
" "?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.

$\text{ } 3 \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times x} 1 \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times \times} 4$
$\text{ } \downarrow \textcolor{w h i t e}{\times} \textcolor{w h i t e}{\times x} \downarrow \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times x} \downarrow$

$\text{ } \times 3 \textcolor{w h i t e}{\times \times} \times 3 \textcolor{w h i t e}{\times \times x} \times 3$
$\text{ } \downarrow \textcolor{w h i t e}{\times} \textcolor{w h i t e}{\times x} \downarrow \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times x} \downarrow$

$\text{ } 9 \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times x} 3 \textcolor{w h i t e}{\times x} : \textcolor{w h i t e}{\times \times} 12$

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

Jul 26, 2017

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: $p e 3 : g r 1 : p r 4$

We are also given that there is a quantity of $12$ pears which we have represented above by $p r 4$.

Then to find the quantity of each fruit we need to multiply the entire ratio by $\frac{\cancel{\left(p r\right) 12}}{\cancel{\left(p r\right) 4}} = 3$

The quantity of each fruit is then: $3 \times \left(p e 3 : g r 1 : p r 4\right)$

$= p e 9 + g r 3 + p r 12$

Now we need some apples.