Question

One number added to three times another number is 24. Five times the first added to three times the other number is 36. find the numbers

Answer 1

To solve this problem, set up a system of equations using the given information. Solve the system using the elimination method, and find the values of the two numbers.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's call the first number x and the second number y.

The first equation states that one number added to three times another number is 24, so we can write it as:

x + 3y = 24

The second equation states that five times the first number added to three times the second number is 36, so we can write it as:

5x + 3y = 36

We have a system of two equations with two variables. We can solve it using substitution or elimination method. Let's use elimination method:

1. Multiply the first equation by 5 to make the coefficients of y the same:
2. 5x + 15y = 120
3. Subtract the second equation from the first equation:
4. (5x + 15y) - (5x + 3y) = 120 - 36
5. 12y = 84
6. Divide both sides by 12:
7. y = 7
8. Substitute the value of y back into one of the original equations (let's use the first equation):
9. x + 3(7) = 24
10. x + 21 = 24
11. Subtract 21 from both sides:
12. x = 3

So, the two numbers are x = 3 and y = 7.