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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
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