Cheryl is 8 more than 2 times as old as Ben. In 16 years, the sum of their ages will be 97. How old is Cheryl now?

Question

This is the question copied exactly from my packet. Help!

Answer 1

When possible, assign a variable to the value the problem asks you to find (so you won't forget to solve for it later).  For this problem,

  Let x = Cheryl's age now

       y = Ben's age now

 

Translate:

  "Cheryl is 8 more than 2 times as old as Ben"    means

      x      =  8     +        2       *                y               [eq1]

 

"In 16 years, the sum of their ages will be 97"    means

                (  x + 16)    +   ( y + 16)   =   97             [eq2]

 

The math:

   ((8 + 2y) + 16)  + (y+16) = 97             [eq2 with substitute for x from eq1]

     3y + 40 = 97                            [collect like terms]

       3y =  57                               [subtract 40 from each side]

        y = 19                            [divide both sides by 3]

 

Put the value of y into either eq1 or eq2 (eq1 may be easier):

    x = 8 + 2(19)

    x = 46

 

Cheryl is 46 and Ben is 19.

Answer 2

The great thing about problems such as this one is that there are many ways to come up with the correct answer. Here is one. Follow along with the steps below the explanation:

 

The easiest way to figure out this problem is to put it into an algebraic equation. Let y represent Ben's current age and x represent Cheryl's current age. x=2y+8, because Cheryl's age(x) is 8 more(+8) than 2 times(2*) Ben's age(y). Now you must determine Ben's current age. For this, use the formula ((97-(16*2))-8)/3=y. Here is why: in 16 years, the sum of Cheryl and Ben's ages will be 97. Because they will each be sixteen years older, you have to remember that this is 16*2 years, or 32 years altogether. This number, which is 65, is the sum of Ben's and Cheryl's ages right now. However, Cheryl is 8 more than 2 times Ben's age, so subtract 8 years, then divide by 3-- 2 parts for Cheryl and 1 part for Ben. This number, 19, is Ben's current age. Now go back to your original formula, x=2y+8, and enter 19 for y. x=2*19+8, or x=46. You can check your work by adding x+y+32=97, or 46+19+32=97, which is correct. See the steps below.

 

 

((97-(16*2))-8)/3=y       Multiply 16*2

   ((97-32)-8)/3=y          Subtract 97-32

      (65-8)/3=y              Subtract 65-8

         57/3=y                Divide 57/3

          19=y

 

        2y+8=x                Enter your value for y

      2*19+8=x              Multiply 2*19

        38+8=x               Add 38+8

          46=x

 

Check your work!

 

x+y+32=97                 Enter your values for x and y

 46+19=97                  Subtract 32 from each side

46+19=65                   Subtract 46 from each side

   19=19

 

Cheryl, or x, is currently 46.

Ben, or y, is currently 19.