Riley had 1/6 as many sports cards as Justin. When Justin gave half of his sports cards to Riley, he had 3 fewer sports cards than his friend. How many sports cards did Justin have at first?
first,
1/6, find out what part is one car
justin gives 1/2 to his friend
then he has 3 fewer
so, if he has three fewer, then how many did he have before he gave any away
r = j/6
j-3 = r+3 - 3
now solve for j
let Riley have x cards, then Justin has 6x cards.
after the gifting:
Justing has 3x cards
Riley has x + 3x or 4x cards
That difference is 3 or
4x - 3x = 3
x = 3
I defined Justin to have 6x cards, so he originally had 18 cards
checking this:
Riley had 3 cards, and Justing had 18
Justing gave half of them or 9 of them to Riley,
so now Justin has 9 and Riley has 3+9 or 12
So he now has 3 more than Justin, my answer is correct
To solve this problem, let's break it down step by step:
Step 1: Let's assume that Justin had x sports cards at first.
Step 2: According to the problem, Riley had 1/6 as many sports cards as Justin. This means that Riley had (1/6) * x cards.
Step 3: When Justin gives half of his sports cards to Riley, he will have x/2 cards left.
Step 4: The problem states that Justin had 3 fewer sports cards than Riley after the exchange. Therefore, we can write the equation:
x/2 = (1/6)*x - 3
Now, let's solve this equation to find the value of x:
Multiply both sides of the equation by 6 to get rid of the fraction:
6 * (x/2) = 6*((1/6)*x - 3)
3x = x - 18
Simplify the equation:
3x - x = -18
2x = -18
Divide both sides of the equation by 2 to solve for x:
x = -18 / 2
x = -9
Since it doesn't make sense to have a negative number of sports cards, we can conclude that there was an error in the problem. Please check the problem statement again to ensure the given information is correct.