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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?

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
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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