Question

The sum of two numbers is 8. Two times the larger number plus four times the smaller number is 8. Find the numbers.

Answer 1

To find the two numbers, set up a system of equations. Solve the equations to find the numbers.

Step-by-step explanation:

To find the two numbers, we can set up a system of equations using the given information.

Let's call the larger number x and the smaller number y.

From the problem, we have the following equations:

x + y = 8

2x + 4y = 8

We can use the first equation to solve for x in terms of y:

x = 8 - y

Substitute this expression for x in the second equation:

2(8 - y) + 4y = 8

Simplify the equation:

16 - 2y + 4y = 8

Combine like terms:

2y = 8 - 16

2y = -8

Divide both sides by 2:

y = -4

Now substitute this value of y back into the first equation to solve for x:

x + (-4) = 8

x = 8 + 4

x = 12

Therefore, the two numbers are 12 and -4.

Answer 2

Answer: 12 and -4

Step-by-step explanation:

Assume the larger number is x and the smaller one is y.

In that case the relevant simultaneous equations are:

x + y = 8

2x + 4y = 8

Use substitution to find relative value of y:

x + y = 8

y = 8 - x

Use to solve equation:

2x + 4y = 8

2x + 4(8 - x) = 8

2x + 32 - 4x = 8

2x - 4x= 8 - 32

-2x = -24

x = -24 / -2

x = 12

y = 8 - x

= 8 - 12

= -4