Braces and Neil share 23 cookies. Braces eats 12 less than 4 times the amount of Neil. How many cookies did each eat?

Question

Braces and Neil share 23 cookies. Braces eats 12 less than 4 times the amount of Neil. How many cookies did each eat?

Answer 1

The trick here is translating English into math. We'll let

 

B be the amount of cookies eaten by Braces, and

N be the amount of cookies eaten by Neil.

 

we know that together they've eaten 23 cookies, so

B + N = 23.

 

Now, for a bit more translation:

"The amount of Neil":                                                 N

"4 times the amount of Neil":                                      4N

"12 less than 4 times the amount of Neil":                   4N - 12

"Braces eats 12 less than 4 times the amount of Neil":      B= 4N - 12

 

Since B = 4N - 12, we can put this in place of B in our first equation:

B + N = 23

(4N - 12) + N = 23.  Now there's only one variable, so we can solve it.  Gather terms:

5N - 12 = 23.  Add 12 to both sides:

5N = 35.  Divide both sides by 5:

N = 7. 

 

Now we know how many cookies Neil ate.  To find out how many Braces ate, substitute this number in place of N.

B + N = 23

B + 7 = 23.  Subtract 7 from both sides:

B = 16.

 

 

Answer 2

Let B be the number of cookies that Braces ate; N be the number of cookies that Neil ate.  They share 23 cookies, so

     B + N = 23

 

"Braces eats 12 less than 4 times the amount of Neil"   means   B = 4*N - 12

"How many cookies did each eat?" means   report B, N

 

      B = 4*N -12

      B = 4*(23-B) - 12    (plugging in the value of N from the first equation)

      B = 92 - 4*B -12

      5*B = 80

      B = 16

Plugging that value into the first equation:

       16 + N = 23

            N = 7  

Checking:

       Is 16 + 7 = 23 ?      yes.

       Is 16 = 4*7 - 12 ?     yes.