jeremy spends 1/4 of his pocket money each week on books.he saves 2/3 of what is left over.if he saves $5 each week,how much weekly pocket money does he receive
x = weekly pocket money
x/4 = weekly amt. spent on books
( x - x/4) = what's left after books
2/3( x - x/4) = 5
Solve for x. Check your answer.
Let's assume Jeremy's weekly pocket money is represented by the variable "x".
According to the given information, he spends 1/4 of his pocket money on books, which means he is left with 3/4 of his pocket money.
Next, he saves 2/3 of what is left over. This means he saves 2/3 * 3/4 of his pocket money.
We are given that he saves $5 each week. So we can set up the following equation:
2/3 * 3/4 * x = $5
Now, let's solve for x.
To simplify the equation, we can cancel out the common factors:
(2/3) * (3/4) = (2 * 3) / (3 * 4) = 6/12 = 1/2
So the equation becomes:
(1/2) * x = $5
To isolate x, we can multiply both sides of the equation by 2:
(1/2) * 2 * x = $5 * 2
x = $10
Therefore, Jeremy receives a weekly pocket money of $10.
To find out Jeremy's weekly pocket money, we'll need to work backward from the information given.
Let's assign a variable to represent Jeremy's pocket money. Let's call it "P".
According to the question, Jeremy spends 1/4 of his pocket money on books each week. This means he has 3/4 (1 - 1/4) of his pocket money left.
After spending on books, he saves 2/3 of what is left over. So, he has 2/3 of 3/4 (2/3 * 3/4) of his pocket money left.
We know that he saves $5 each week, so we can set up the equation:
(2/3) * (3/4) * P = $5
Now, let's solve for P (Jeremy's pocket money):
(2/3) * (3/4) * P = $5
Multiplying the denominators gives:
(2/3) * (3/4) * P = $5
(6/12) * P = $5
Simplifying the left side of the equation:
(1/2) * P = $5
To isolate P, we'll multiply both sides of the equation by 2:
(1/2) * P * 2 = $5 * 2
P = $10
Therefore, Jeremy receives $10 as his weekly pocket money.