Answer:
Smaller number: 12
Greater number: 31
Step-by-step explanation:
Hi there!
Let x equal to the smaller number.
Let y be equal to the greater number.
1) Translate the information into equations
"One is 7 more than twice the other"
⇒ [tex]y=2x+7[/tex]
"The sum of the numbers is 43"
⇒ [tex]x+y=43[/tex]
2) Use substitution to solve for the smaller number
[tex]x+y=43[/tex]
Plug the equation [tex]y=2x+7[/tex] into the above equation
[tex]x+(2x+7)=43\\x+2x+7=43\\3x+7=43[/tex]
Subtract both sides by 7
[tex]3x+7-7=43-7\\3x=36[/tex]
Divide both sides by 3 to isolate x
[tex]\frac{3x}{3} = \frac{36}{3} \\x=12[/tex]
Therefore, the smaller number equates to 12.
3) Use substitution to solve for the greater number
[tex]x+y=43[/tex]
Plug in x as 12
[tex]12+y=43[/tex]
Subtract both sides by 12 to isolate y
[tex]12+y-12=43-12\\y=31[/tex]
Therefore, the greater number equates to 31.
I hope this helps!
