Joel bought a bag with (2/9) of his money and a pair of shoes which cost $40 more than the bag. He had (1/3) of his money left.
a) How much did the bag cost?
b) how much did he have at first?
if he had 1/3 left, then he had spent 2/3
So, if the original amount of money was x, then
2/9 x + (2/9 x + 40) = 2/3 x
4/9 x + 40 = 6/9 x
2/9 x = 40
Now you can easily answer the questions.
Yes, I believe that works... for you... but I still don't understand the concept
Please help... thank you very much
Let's assume that the amount of money Joel had initially is represented by 'x'.
a) To find the cost of the bag, we multiply the fraction (2/9) by the total amount of money he had initially, which is 'x'.
Cost of the bag = (2/9) * x
b) After buying the bag, he had (1 - 2/9) = (7/9) of his money left.
He then spent an additional $40 on a pair of shoes, which means he had (7/9) * x - $40 left.
We are given that (7/9) * x - $40 is equal to (1/3) of his initial money. So we can set up the equation:
(7/9) * x - $40 = (1/3) * x
To solve this equation and find the value of 'x', we can start by eliminating the fractions by multiplying both sides by 9*3 = 27:
27 * [(7/9) * x - $40] = 27 * (1/3) * x
Simplifying:
27 * (7/9) * x - 27 * $40 = 9 * x
(7/3) * 27 * x - 27 * $40 = 9 * x
7 * 9 * x - 27 * $40 = 9 * x
63 * x - 27 * $40 = 9 * x
Subtracting 9 * x from both sides:
63 * x - 9 * x = 27 * $40
54 * x = 27 * $40
Dividing both sides by 54:
x = (27 * $40) / 54
Therefore, the initial amount of money Joel had, 'x', is (27 * $40) / 54.
Now, we can substitute this value of 'x' back into the cost of the bag equation from part a) to find the cost of the bag.
To find the cost of the bag and how much Joel had at first, we can solve this problem step by step.
Let's assume Joel's initial amount of money is "x" dollars.
a) How much did the bag cost?
The problem states that Joel bought a bag with (2/9) of his money. We can calculate the cost of the bag by multiplying his initial amount of money by (2/9).
Cost of the bag = (2/9) * x
b) How much did he have at first?
The problem also states that Joel had (1/3) of his money left after buying the bag and a pair of shoes. To find the remaining amount, we need to subtract the cost of the bag and the cost of the shoes from his initial amount of money.
Remaining amount = x - ((2/9) * x + (2/9) * x + $40)
= x - (4/9) * x - (4/9) * x - $40
= x - (8/9) * x - $40
Now, we know that the remaining amount is (1/3) of his initial amount, so we can set up an equation:
x - (8/9) * x - $40 = (1/3) * x
Let's solve this equation to find the value of x, which represents Joel's initial amount of money.
Combining like terms, we have:
(9/9) * x - (8/9) * x = $40 + (1/3) * x
(1/9) * x = $40 + (1/3) * x
To get rid of the fractions, we can multiply the entire equation by 9:
x = 9 * ($40 + (1/3) * x)
x = $360 + (3/3) * x
x - (3/3) * x = $360
(1/3) * x = $360
To solve for x, we can multiply both sides of the equation by 3:
x = $360 * 3
x = $1080
So, Joel had $1080 at first.
Now, let's calculate the cost of the bag using the initial amount:
Cost of the bag = (2/9) * $1080
= $240
Therefore, the bag cost $240.