Word Problem Help

Question

Adam spent $7 less than 4/5 of his money on a notebook and $4 more than 3/7 of his remaining money on a pencil. If he was still left with $12, find the price of each item

Answer 1

Let N be the cost of the Notebook,

Let P be the cost of the Pencil.

Let M be the Money that he had.

The Notebook cost 4/5 of his Money less $7:

N = 4/5 of M - 7

N = 4/5 * M - 7

The Pencil cost 3/7 of the remaining of his Money, plus $4.

The remaining of his Money is: 1/5 of M.

So, the Pencil cost:

P = 3/7 of 1/5 of M + 4

P = 3/7 * 1/5 * M + 4

After buying the Notebook and the Pencil, he was still left with $12, so:

N + P = M - 12

Replacing N and P in the last equation:

(4/5 * M - 7) + (3/7 * 1/5 * M + 4) = M -12

4/5 * M - 7 + 3/7 * 1/5 * M + 4 = M - 12

(4/5)M - 7 + (3/35)M + 4 = M - 12

(4/5)M + (3/35)M - M = -12 + 7 - 4

(4/5 + 3/35) M - M = -9

(31/35)M - M = -9

(-4/35)M = -9

M = (-9) * (-35/4)

M = 78.75

Replacing for N:

N = 4/5 of M - 7

N = (4/5) * (78.75) - 7

N = 63 - 7

N = 56

Replacing for P:

P = 3/7 of 1/5 of M + 4

P = (3/7) * (1/5) * (78.75) + 4

P = (3/35) * ( 78.75) + 4

P = 6.75 + 4

P = 10.75

Checking your work:

N + P = M - 12

56 + 10.75 = 78.75 - 12

66.75 = 66.75

So, the Notebook cost $56 and the Pencil cost $10.75

Answer 2

note book=(x*.8-7)-pencils=(.42857(x*.8-7)+4)=x-12

(.8x -7)-(.42857*.8x-7)+16=x

(.8x-7)-.3428x +9 =x

.45714x+2=x

.-x+.45716x=-2

-.54285x=-2

2/.54285=x

x=-3.68421........

Substitute