Grandma gave some cards to Ritchie and some to Erin. She gave 6 times the amount to Erin as she did to Ritchie. If the total amount she gave them was 280 cards, how many did she give to Ritchie?

Let x = the number of cards Grandma gave to Ritchie

Let y = the number of cards Grandma gave to Erin

Since we have two unknowns (x and y) we need two equations relating the unknowns to solve the problem.

Equation 1:

*She gave 6 times the amount to Erin (y) as she did to Ritchie (x):*y = 6xEquation 2:

*the total amount she gave them was 280 cards*: x + y = 280Now substitute the y in equation 2 with 6x from equation 1:

x +

**y**= 280 [Equation 2]x +

**6x**= 280 [Since y=6x, replace the y in equation 2 with 6x]7x = 280

Solve for x