NEED HELP WITH THIS THANKS!!!TOGETHER, RYAN AND MAX HAD 195 BASEBALL CARDS. ONCE MAX GAVE 3/8 OF HIS CARDS TO ANOTHER FRIEND, HE AND RYAN HAD AN EQUAL NUMBER OF CARDS. HOW MANY MORE CARDS DID MAX HAVE THAN RYAN IN THE BEGINNING?
1 3/8x + x = 195
Solve for x.
Please don't use all caps.
9times14
Let's solve this step-by-step.
Step 1: Let's assume that Ryan had x number of baseball cards.
Step 2: Since Ryan and Max had a total of 195 baseball cards, Max would have had (195 - x) cards.
Step 3: Max gave away 3/8 of his cards, which means he kept (1 - 3/8) = 5/8 of his original cards.
Step 4: Since after giving away his cards, Max and Ryan had an equal number of cards, we can set up the following equation:
x = (5/8)(195 - x)
Step 5: Let's solve the equation:
Multiply both sides of the equation by 8 to get rid of the fraction:
8x = 5(195 - x)
Distribute 5 on the right side:
8x = 975 - 5x
Add 5x to both sides:
8x + 5x = 975
Combine like terms:
13x = 975
Divide both sides by 13:
x = 975/13
Simplify the fraction:
x = 75
Step 6: Now, we know that Ryan had 75 cards. Let's find out how many cards Max had in the beginning:
Max = 195 - x = 195 - 75 = 120
Step 7: Finally, let's calculate how many more cards Max had than Ryan in the beginning:
Max - Ryan = 120 - 75 = 45
So, Max had 45 more cards than Ryan in the beginning.
To solve this problem, let's break it down into steps:
First, let's represent the unknown quantities in the problem:
Let's assume that Ryan had x cards initially, and Max had y cards initially.
According to the problem, together Ryan and Max had 195 baseball cards:
x + y = 195 -- Equation 1
Now, Max gave away 3/8 (or 3 out of every 8 cards) to another friend. That means Max kept 5/8 (or 5 out of every 8 cards) for himself.
So, the quantity of cards Max kept would be 5/8 of his initial cards:
(5/8) * y = (5y/8) -- Equation 2
After giving away 3/8 of his cards, Max and Ryan had an equal number of cards. So, Max had (5y/8) cards and Ryan also had (5y/8) cards:
x = (5y/8) -- Equation 3
We now have a system of two equations with two variables (Equation 1 and Equation 3). Let's solve this system to find the values of x and y.
From Equation 1, we can express x in terms of y:
x = 195 - y
Substituting the value of x into Equation 3:
195 - y = (5y/8)
To solve for y, we can cross-multiply:
8(195 - y) = 5y
Expanding the equation:
1560 - 8y = 5y
Moving all y terms to one side:
13y = 1560
Dividing by 13:
y = 120
Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:
x = 195 - y
x = 195 - 120
x = 75
So, Ryan initially had 75 cards and Max initially had 120 cards.
To find how many more cards Max had than Ryan in the beginning, we subtract Ryan's initial number of cards from Max's initial number of cards:
Max's initial cards - Ryan's initial cards = 120 - 75 = 45
Therefore, Max initially had 45 more cards than Ryan.