Expert: Bobby Soltani - 9/5/2006

Question
I would appreciate it very much if you could help me with a word problem that requires using a variable in order to solve.  I'm not sure how to set up the equation.

"Tom has 9 more baseball cards than Ken and Jill has 3 less than Randy.  If Randy has 4 more cards than Ken, could the total numbers of cards they have be 45?"

Thank you!
Meagan  

Answer
Hi Meagan,

Let the number of cards that Tom has be t, ken is k, jill j, and randy r.

Tom has 9 more than Ken

t = k + 9

Jill has 3 less than Randy

j = r - 3

Randy has 4 more than k

r = k + 4

Could the total be 45

t + k + j + r = 45

let's try to get the last equation to only have the variable k.

replace t with k + 9

k + 9 + k + j + r = 45

replace r with k + 4

k + 9 + k + j + k + 4 = 45

j = r - 3 and r = k + 4, so j = (k + 4) - 3 = k + 1

replace j with k + 1

k + 9 + k + k + 1 + k + 4 = 45

combine the k terms and the constants

4k + 14 = 45

subtract 14 from both sides

4k = 31

divide both sides by 4

k = 31/4 = 7.75

Since they can't have .75 of a card, it looks like they can't have a total of 45 cards.

Let me know if you have any questions.

Bobby