math answer

Question

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?

Answer 1

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 = 6x

 

Equation 2: the total amount she gave them was 280 cards:  x + y = 280

 

Now 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