Question

The sum of two numbers is 42. The smaller number is 22 less than the larger number. What are the numbers?Larger number:Smaller number:

Answer 1

Larger number:32

Smaller number:10

Explanation

Step 1

set the equations

let x represents the larger number

let y represents the smaller number

so

a)The sum of two numbers is 42

rewrite

$x+y=42\Rightarrow equation(1)$

b)the smaller number is 22 less than the larger number( in other words you have to add 22 to the smaller number to get the larger one)

so

$x=y+22\Rightarrow equation(2)$

Step 2

Solve the equations

a)replace the x value form equation (2) into equation(1)

hence

$\begin{gathered} x+y=42\Rightarrow equation(1) \\ (y+22)+y=42 \\ \text{add like terms} \\ 2y+22=42 \\ \text{subtract 22 in both sides} \\ 2y+22-22=42-22 \\ 2y=20 \\ \text{divide both sides by 2} \\ \frac{2y}{2}=\frac{20}{2} \\ y=10 \end{gathered}$

therefore

the smaller number is 10

now, replace the y value into equation(1)

$\begin{gathered} x+y=42\Rightarrow equation(1) \\ \text{replace} \\ x+10=42 \\ \text{subtract 10 in both sides} \\ x+10-10=42-10 \\ x=32 \end{gathered}$

hence

the larger number is 32

I hope this helps you

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