 # the ratio of doors to windows is 2:4. There are 48 doors and windows in a building. how many doors are there? How many windows are there?​

Math

## Question

the ratio of doors to windows is 2:4. There are 48 doors and windows in a building. how many doors are there? How many windows are there?​

## RATIO

### Solve:

Identify the x that is multiplied to each number in the fraction will have a total of 48.

$$\implies \sf \large2 \: : \: 4$$

$$\implies \sf \large2x + 4x = 48$$

$$\implies \sf \large6x = 48$$

$$\implies \sf \large \frac{ \cancel6x}{ \cancel6} = \frac{48}{6} \\$$

$$\implies \sf \large \therefore \: x = 8$$

$$\:$$

Use 8 as the value of x to check and find how many doors and windows are there.

$$\implies \sf \large2(8) + 4(8) = 48$$

$$\implies \sf \large16 + 32 = 48$$

$$\implies \sf \large48= 48 \rightarrow \tt \green{true}$$

### $$\:$$

$$\sf \large \implies \huge \orange{16 \: doors}$$

$$\sf \large \implies \huge \orange{32 \: windows}$$

### ==============================

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## Problem:

the ratio of doors to windows is 2:4. There are 48 doors and windows in a building. how many doors are there? How many windows are there?

## Solution:

$$\green{ \frac{48}{2 + 4} }$$

$$= \frac{48}{6}$$

$$= 8$$

$$8 \times 2 = \boxed{16}$$

$$8 \times 4 = \boxed{32}$$

$$16 + 32 = \underline{48}$$