the sum of two numbers is 20. the difference between three times the first number and twice the second is 40. find the two numbers

Question

word problem

Answer 1

Here's what we know:

a + b = 20

3a - 2b  = 40

 

We can solve this with the elimination method. Multiply the first equation by 2:

2a + 2b = 40

3a - 2b = 40

-------------------

5a = 80

Divide by 5:

a = 16

 

Now we can find b:

16 + b = 20

b = 4

 

check:

16 * 3 - 2 * 4 = 40

48 - 8 = 40

40 = 40