Answered: Mark spent 3/8 of his money on 3 pens…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter4: Polynomials

Section4.10: Problems Without Solutions

Problem 15P

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Question

Mark spent 3/8 of his money on 3 pens and 4 sharpeners. A sharpener costs 3/4 as much as a pen. What is the maximum number of sharpeners he can buy with his remaining money?

Expert Solution

Step 1

Given:

Let's take the total money as x, pens as p and sharpeners as s.

Money spent on 3 pens and 4 sharpeners is,

$\frac{3}{8} x = 3 p + 4 s . . . . . . . . . (1)$

Cost of sharpener is 3/4 as much as pen.

$s = \frac{3}{4} p p = \frac{4}{3} s$

Step 2

Substitute p in (1)

$\frac{3}{8} x = 3 (\frac{4 s}{3}) + 4 s \frac{3}{8} x = 4 s + 4 s \frac{3}{8} x = 8 s$

So, with 3/8 of total money he can buy 8 sharpeners.

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