IDNLearn.com offers a comprehensive solution for all your question and answer needs. Join our platform to receive prompt and accurate responses from experienced professionals in various fields.

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:

Sagot :

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

[tex]x+y=42\Rightarrow equation(1)[/tex]

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

[tex]x=y+22\Rightarrow equation(2)[/tex]

Step 2

Solve the equations

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

hence

[tex]\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}[/tex]

therefore

the smaller number is 10

now, replace the y value into equation(1)

[tex]\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}[/tex]

hence

the larger number is 32

I hope this helps you

x

Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.