Honors algebra

Question

our question is this:

A number is 5 more than 4 times another. The greater number decreased by 2/3 the smaller equals 20. What are the two numbers. 

We are struggling with how to set up the equation  We were given the answers and there are two options:  -51 & -14 or 4.5 & 23

Answer 1

n = one number

m = the other number

 

(i)  n = 4m + 5

 

If n > m, then

 

(ii)  n - (2/3)m = 20

 

Plug n from (i) into (ii) and solve for m.  That gives m = 4.5, which you plug into (i) and get n = 23.

 

But if m > n, then

 

(i) is still true

 

(ii)  m - (2/3)n = 20

 

Plug n from (i) into (ii), and get m = -14.  Plug this value of m into (i) and get n = -51.

 

There are your 2 options.

 

 

 

 

 

Answer 2

Both choices work. 4(4.5) + 5 = 23 18 + 5 = 23 23 = 23 True 23 - (2/3)4.5 = 20 23 - 3 = 20 20 = 20 True Do the same for the other set. Remember that -14 is the greater number.

Answer 3

n represents a number

4n + 5 represents the second number

 

(4n + 5) - (2/3)n  = 20

 

Can you solve for n and answer?