The sum of four times a number and another number is 10. The difference of the two numbers is 35. What is the larger number? Also please explain how you got that answer

Question

asked Jun 5, 2021 190k views

2 Answers

Chambeur · Answer 1 · 2021-06-09T10:12:53+0000

Answer:

The two numbers are 9 and -26.

The larger number is 9.

Explanation:

Let the two unknown numbers be x and y.

The sum of a four times a number x and another number y is 10. Hence:

4x+y=10

And the difference between the two numbers is 35. So:

x-y=35

So, we have the system of equations:

$\left\{ \begin{array} \ 4x+y=10 \\ x-y=35 \end{array}$

From the second equation, we can add y to both sides:

x=y+35

Now, we can substitute this into the first equation:

4(y+35)+y=10

Distribute:

4y+140+y=10

Simplify:

5y+140=10

Subtract 140 from both sides:

5y=-130

Divide both sides by 5:

y=-26

So, the value of y is -26 .

Then it follows that the value of x is:

x=y+35

Substitute -26 for y:

x=-26+35=9

So, our two numbers are 9 and -26.

The larger number is 9.

So, our answer is 9.