Question

What are the two numbers if the larger number is two more than five times the smaller number, and their sum is 80?

A) 15 and 65
B) 20 and 60
C) 25 and 55
D) 30 and 50

Answer 1

To find the two numbers, we can set up a system of equations using the information given. Using substitution method, we can solve for the two numbers to be 13 and 67.

Step-by-step explanation:

To solve this problem, let's call the smaller number x and the larger number y. We are given that the larger number is two more than five times the smaller number, so we can write the equation y = 5x + 2. We are also given that the sum of the two numbers is 80, so we can write the equation x + y = 80.

Now we have a system of two equations: y = 5x + 2 and x + y = 80. We can solve this system using substitution or elimination.

Let's solve it using substitution. We can substitute the expression for y from the first equation into the second equation: x + (5x + 2) = 80. Simplifying this equation, we get 6x + 2 = 80. Subtracting 2 from both sides, we get 6x = 78. Dividing both sides by 6, we get x = 13.

Now we can substitute the value of x back into either of the original equations to find the value of y. Let's substitute it into y = 5x + 2: y = 5(13) + 2. Calculating this, we get y = 65 + 2 = 67.

So the two numbers are 13 and 67.