URGENT the larger of two numbers is two more than five times the smaller number. if the sum of the two numbers is 80 , find both numbers.

Answer 1

Hi Victoria!

To approach this problem, define your numbers as variables, set up an equation, and then solve.

Let's first define the smaller number as x.

The problem says, "the larger of the two numbers is two more than five times the smaller number". So we can set the larger number as 5x+2.

To set up the equation, the problem then tells us "the sum of the two numbers is 80". So we can add both of our variables and set it equal to 80, giving us the equation:

x + (5x+2) = 80

Simplifying this equation and solving for x, we get

6x + 2 = 80 (adding the x varibles)

6x = 78 (subtracting each side by 2)

x = 13 (dividing each side by 6)

We now know the smaller of the two numbers is 13. To solve for the larger number, we plug the x-value in to our equation for the larger number:

5x + 2 = 5*(13) + 2 = 65 + 2 = 67

To check our work, we can see the the two numbers (13 and 67) add up to 80!

Let me know if you have any questions. I hope this helps!

Best,

Stephanie

Answer 2

We're dealing with 2 different equations here.

y = 5x + 2

x + y = 80

We already know what y is for the first equations, and we can find it for the second one by subtracting x from both sides. Then we would get:

y = 5x + 2

y = 80 - x

Since they're both equal to y, they are equal to each other

5x + 2 = 80 - x

From there, we can put all the x's on once side and the numbers on the other

6x + 2 = 80

6x = 78

x = 13

Since we know x = 13 and x + y = 80, we can find y by subtracting x

y = 80 - 13

y = 63