Question

Given two consecutive integers. The sum of four times the first integer and six times the second integer is 96. Find the integers.

Find the First Integer and Second Integer

Answer 1

Hey there! I'm happy to help!

If these are consecutive integers it means that they are one apart. Let's call our numbers x and y and create a system of equations. Our x will be the first integer and y will be the second.

y=x+1

4x+6y=96

We plug our y value into the second equation to solve for x.

4x+6(x+1)=96

We use the distributive property to undo the parentheses.

4x+6x+6=96

We combine like terms.

10x+6=96

We subtract 6 from both sides.

10x=90

And divide both sides by 10.

x=9

Since y is x+1, we know that y is 10.

Our integers are 9 and 10.

Have a wonderful day! :D