Question

Anne is twice as old as Bill, and Bill is 3 years older than Christie. The sum of Anne s and Christie s ages equal 72. Find their age difference.?

Answer 1

Answer:

26 years

Step-by-step explanation:

All you have to do here is create a few equations to help you out. We'll use the variables A, B, and C to match their first initials.

If Anne is twice as old as Bill, then you can say Bill's age must equal 2A (double Anne's age). So, we have B = 2A. Next, Bill is 3 years older than Christie, so translating that into math symbols, we can say B = 3 + C. Lastly, Anne and Christie's ages equal 72, so A + C = 72. Let's line those up:

B = 2A

B = 3 + C

A + C = 72

Since you have two equations that say B = ... you can combine those into one. If B equals both 2A and 3 + C, then those two values must equal each other:

EQUATION 1: 3 + C = 2A

EQUATION 2: A + C = 72

From here, you can solve this any way you want. The easiest way is to solve for one variable and plug it into the other:

3 + C = 2A ... add 3 to both sides

C = 3 + 2A ... now plug this into the second equation

A + (3 + 2A) = 72

Now we only have one variable to deal with, so you can get Anne's age pretty easily. Simplify.

3A + 3 = 72

3A = 69

A = 23

Now you have Anne's age, so go back to either EQUATION 1 or EQUATION 2 above and plug in your A-value.

23 + C = 72

C = 49

And lastly, we want to find Bill's age. Read the problem again, and see that Bill is 3 years older than Christie. This makes Bill 52, but we don't need that for the final answer. To find Anne and Christie's age difference, all you do is take 49 - 23 = 26. They are 26 years apart.