Isaiah and Andy had a total of 560 trading cards. After Isaiah gave1/9 of cards to Andy they had an equal # of trading cards. How many more cards did isiah have than Andy at the beginning?
Isaiah: X cards.
x-x/9 = 560/2
8x/9 = 280
8x = 2520
X = 315
560 - 315 = 245 More than Andy.
Let's break down the problem step by step:
Step 1: Set up the equation.
Let's assume Isaiah had x trading cards at the beginning. So, Andy had (560 - x) trading cards. After Isaiah gave 1/9 of his cards to Andy, both of them had an equal number of trading cards.
Therefore, the equation becomes:
x - (1/9)x = (560 - x) + (1/9)x
Step 2: Simplify the equation.
Let's simplify the equation by combining like terms on both sides:
(8/9)x = 560
Step 3: Isolate x.
To isolate x, we multiply both sides of the equation by 9/8:
x = (9/8) * 560 = 630
Step 4: Calculate the difference between Isaiah and Andy initially.
To calculate the difference between Isaiah and Andy initially, we subtract the number of trading cards Andy had (560 - x = 560 - 630 = -70).
However, the result is negative, indicating that Andy had more trading cards initially.
Therefore, there were no trading cards that Isaiah had more than Andy at the beginning.
To solve this problem, we need to break it down into steps:
Step 1: Understand the problem.
Isaiah and Andy had a total of 560 trading cards. After Isaiah gave 1/9 of his cards to Andy, they ended up with an equal number of trading cards. We need to find out how many more cards Isaiah had than Andy at the beginning.
Step 2: Assign variables.
Let's assign variables to the unknowns in the problem:
Let's say Isaiah had x trading cards.
And let's say Andy had y trading cards.
Step 3: Form equations based on the information given.
According to the problem, the total number of trading cards they had in the beginning was 560:
x + y = 560 ---- Equation 1
After Isaiah gave 1/9 of his cards to Andy, they had an equal number of trading cards. This means that y should be increased by 1/9 of x:
Isaiah's remaining cards = x - (1/9)x = 8/9x
Andy's cards = y + (1/9)x
At this point, since they have an equal number of cards, we can set up an equation:
8/9x = y + (1/9)x ---- Equation 2
Step 4: Solve the equations.
We have two equations:
x + y = 560 ---- Equation 1
8/9x = y + (1/9)x ---- Equation 2
To solve these equations, we can substitute Equation 2 into Equation 1:
x + 8/9x = 560
Multiplying both sides by 9 to eliminate the fraction:
9x + 8x = 5040
17x = 5040
Dividing both sides by 17:
x = 5040/17
x ≈ 296.47
Now that we know Isaiah started with approximately 296.47 cards, we can find Andy's starting number by substituting this value into Equation 1:
296.47 + y = 560
y = 560 - 296.47
y = 263.53
Step 5: Calculate the difference.
To find out how many more cards Isaiah had than Andy at the beginning, we subtract y from x:
Difference = x - y
Difference = 296.47 - 263.53
Difference ≈ 32.94
So, Isaiah had approximately 32.94 more cards than Andy at the beginning.