Fred was given some pocket money. He spent 1/3 of his money to buy games and saved 2/3 of the remainder. He used the rest of the money on food. If he spent $120 altogether, how much did he save?
x to start
1/3 x spent on games, leaving 2/3 x
4/9 x saved, leaving 2/9 x
x/3 + 2/9 x = 120
5/9 x = 120
4/9 x = 96 was saved
Let's say the total amount of pocket money Fred was given is represented by 'x'.
Fred spent 1/3 of his money to buy games, so he spent x * 1/3 = x/3 on games.
After spending on games, he had x - x/3 = 2x/3 remaining.
Fred saved 2/3 of the remainder, so he saved (2x/3) * 2/3 = 4x/9.
He used the rest of the money on food, which means he spent the remaining (2x/3) - (4x/9) = 2x/9 on food.
According to the question, the amount he spent on games, savings, and food added up to $120.
So, we can write the equation: x/3 + 4x/9 + 2x/9 = 120.
To solve for x, we can first simplify the equation:
9x/27 + 12x/27 + 6x/27 = 120
(9x + 12x + 6x) / 27 = 120
27x / 27 = 120
x = 120
Therefore, Fred was given $120 as his total pocket money.
To find out how much he saved, substitute the value of x in the equation we derived earlier:
4x/9 = 4 * 120 / 9 = 480 / 9 = $<<480/9=53.333333333333336>>53.33 (approx.)
So, Fred saved $53.33.
To find out how much Fred saved, we need to follow a step-by-step calculation.
Step 1:
Let's assume Fred's total pocket money as "x" dollars.
Step 2:
Fred spent 1/3 of his money to buy games, which means he has (2/3) * x dollars remaining.
Step 3:
Out of the remaining money, Fred saved 2/3 of it, which means he spent (1 - 2/3) = 1/3 of it on food.
Step 4:
From the problem, we know that Fred spent a total of $120. So, we can equate the amount he spent on games and food to $120.
(1/3) * x + (1/3) * [(2/3) * x] = $120
Step 5:
Simplifying the equation:
(1/3) * x + (2/9) * x = $120
Simplifying further:
(3/9) * x + (2/9) * x = $120
(5/9) * x = $120
Step 6:
To isolate x, the variable representing the total pocket money, we multiply both sides of the equation by the reciprocal of (5/9), which is (9/5):
[(9/5) * (5/9)] * x = (9/5) * $120
x = (9/5) * $120
x = $216
Step 7:
Now that we know Fred's total pocket money is $216, we can calculate how much he saved.
Fred saved 2/3 of the remainder after buying games:
(2/3) * [(2/3) * $216] = (2/3) * $144 = $96
Therefore, Fred saved $96.