Question

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

Answer 1

Yup answers 9

Step-by-step explanation: just took the test

Answer 2

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.