. How many baseball cards does Michelle have?

Question

Michelle has less than 50 baseball cards. If she puts them in packs of 7, she has 5 baseball cards left. If she puts them in packs of 9, she has 6 baseball cards left. How many baseball cards does Michelle have?

Answer 1

Ok! Looks like we have ourselves a fun little equation here!

 

If she puts them in packs of 7, there will be 5 left over, so if we use 'x' to represent the number of packs she makes, we can consider that situation to me "7x + 5" (x number of packs of 7, with 5 left over). Similarly, for the packs of 9, we get "9y + 6" (y number of packs of 9, with 6 left over. We have to use different letters x and y because there's going to be a different number of packs in each case).

 

 > That was the hard part, all downhill from here!

If you had a graphing calculator, this part would be super easy. But, let's pretend you don't and want to work it out the easiest manual way possible.

So, 7x + 5 < 50

7x < 45

So x can be 1, 2, 3, 4, 5, or 6

If x was 6, she'd have 49 cards. Could that fit the other half of our equation? 9y + 6 = 49?    9y = 43? NOPE

If x was 5, she'd have 40 cards. Could that fit the other half of our equation? 9y + 6 = 40? 9y = 34? NOPE

If x was 4, she'd have 33 cards. Could that fit the other half of our equation? 9y + 6 = 33? 9y = 27? YES! That goes in evenly.

 

TADA! 33 cards

 

 

Answer 2

In groups of 7, with 5 left over, she must have one of the following amounts:

 

1*7 + 5 = 12

2*7 + 5 = 19

3*7 + 5 = 26

...

 

Continue until the total is more than 50.

 

In groups of 9, with 6 left over, you can do the same thing:

1*9 + 6 = 15

...

 

The number that is in both lists must be the amount of cards she has!