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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

User Nick Hill
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2 Answers

2 votes

Answer:

Yup answers 9

Step-by-step explanation: just took the test

User Dakadaka
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2 votes

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.

User Chambeur
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