Jerry spent 1/5 of his allowance on a book and 3/8 of the remainder of his allowance for a pen.jerry remained with $12.00.calculate:
(A)jerry's allowance.
(B)the cost of the book.
(C)the cost of the pen.
1/5 x + 3/8(4/5 x)
x - 1/5 x - 3/8 (4/5 x) = 12.00
x - 1/5 x - 3/10 x = 12.00
10/10 x - 2/10 x - 3/10 x = 12
5/10 x = 12 x = 24
1/5 (24) = $ 4.80 on book
3/8 (19.80) =7.20
check 24 - 4.80 - 7.20 = 12
Let's solve the problem step by step:
(A) To calculate Jerry's allowance, we need to find the total amount he has left after buying the book and the pen. We know that he had $12.00 remaining after buying the pen.
Let's work backward to find the remainder of his allowance. 3/8 of the remainder is equal to $12.00, so to find the full remainder, we can multiply $12.00 by 8/3.
($12.00) x (8/3) = $<<12*8/3=32.00>>32.00
Now, since 1/5 of his allowance was spent on the book, we can find the total allowance by dividing $32.00 by 4/5 (1 - 1/5 = 4/5).
($32.00) รท (4/5) = $<<32/(4/5)=40.00>>40.00
Therefore, Jerry's allowance is $40.00.
(B) To find the cost of the book, we know that Jerry spent 1/5 of his allowance.
($40.00) x (1/5) = $<<40*1/5=8.00>>8.00
So, the cost of the book is $8.00.
(C) To find the cost of the pen, we already know that it is $12.00 since Jerry was left with that amount after purchasing it.
Therefore, the cost of the pen is $12.00.
To summarize:
(A) Jerry's allowance is $40.00.
(B) The cost of the book is $8.00.
(C) The cost of the pen is $12.00.
To solve this problem, we will follow a step-by-step approach:
Step 1: Assign variables
We will assign variables to the unknown quantities:
Let x be Jerry's allowance.
Let C be the cost of the book.
Let P be the cost of the pen.
Step 2: Calculate the portion spent on the book
Jerry spent 1/5 of his allowance on a book, so the amount spent on the book is given by: (1/5) * x.
Step 3: Calculate the remaining allowance
The remainder of Jerry's allowance after buying the book is given by: (x - (1/5) * x).
Step 4: Calculate the portion spent on the pen
Jerry spent 3/8 of the remaining allowance on a pen, so the amount spent on the pen is given by: (3/8) * (x - (1/5) * x).
Step 5: Calculate the remaining amount after buying the pen
The remaining amount Jerry has after buying the pen is given by: (x - (1/5) * x) - (3/8) * (x - (1/5) * x).
According to the problem, Jerry has $12.00 left, so we can set up an equation:
[(x - (1/5) * x) - (3/8) * (x - (1/5) * x)] = 12.00.
Now, let's solve this equation to find the answers:
(A) Jerry's allowance:
To find Jerry's allowance, we solve the equation:
[(x - (1/5) * x) - (3/8) * (x - (1/5) * x)] = 12.00.
Simplify the equation:
[(4/5) * x - (3/8) * (4/5) * x] = 12.00.
Multiply through by 40 to clear the denominators:
32x - (3 * 8 * x) = 480.
32x - 24x = 480.
8x = 480.
x = 480 / 8.
x = 60.
Jerry's allowance is $60.00.
(B) The cost of the book:
The cost of the book is (1/5) * x = (1/5) * 60 = 12.00.
The cost of the book is $12.00.
(C) The cost of the pen:
The cost of the pen is (3/8) * (x - (1/5) * x) = (3/8) * (60 - (1/5) * 60) = (3/8) * (60 - 12) = (3/8) * 48 = 18.00.
The cost of the pen is $18.00.
So, the answers are:
(A) Jerry's allowance is $60.00.
(B) The cost of the book is $12.00.
(C) The cost of the pen is $18.00.