Can you help me on this question please!!!!!

Question

The second number is five times the first number and twice their sum is forty eight. Let x be the first number and y the second number. What are the two numbers?

Answer 1

x = first number

y = second number

Let's turn sentences into equations!

The second number is five times the first number -- > y = x * 5 -------- 1

twice their sum is forty eight ------------------------------ > (x+y) * 2 = 48 --------- 2

Now we have two equations to solve and two unknown x and y. Lets start!

y = 5x

(x+y) * 2 = 48

Substitute y = 5x to Eq. 2. Then solve for x .

(x+5x) * 2 = 48

6x * 2 = 48

x = 4

Now we find y from Eq. 1

y = 5*4

y = 20

Answer 2

When doing these types of problems, it is helpful to turn them into formulas to solve.

Let us first transform the first section, 5x = y

And the second, 2(x + y) = 48

Now that we have both of the equations set up, let us substitute the first equation (5x = y) into the second (2(x + y) = 48).

2(x + 5x) = 48

2x + 10x = 48

12x = 48

x = 4

Now let us use x to solve for y using either equation. I will use the 1st one.

5(4) = y

y = 20

∴ y = 20, x = 4