Question 1172306
Hi
Bob spent 50 dollars on pens and markers. The ratio of money spent on pens pencils and markers was 4:5:1. Pens were sold at 3 for a dollar. The number of pencils he bought was 1/6 of the number of pens. The number of markers he bought was 2/5 of the number of pencils. 
How many pens and markers did he buy.
How many pencils could he buy for 175 dollars. Thanks 
<pre>Let multiplicative factor-cost be x
Then amount spent on pens, pencils, and markers = 4x, 5x, and x, respectively
Total amount spent on all 3 items = 4x + 5x + x = 10x

Amount spent on pens, and on markers = 4x, and x, respectively, so total = 4x + x = 5x
Also, itw’s given that $50 was spent on pens and markers, and so, we get:  5x = 50
Multiplicative factor, or {{{matrix(1,5, x, "=", 50/5, "=", 10)}}}

With multiplicative factor, x, being 10, amount spent on pens = 4(10) = $40
This means that amount spent on markers = $50 - $40 = $10
In addition, amount spent on pencils = 10x - 50, or 10(10) - 50 = 100 - 50 = $50


Amount spent on pens = $40, and with 3 pens costing $1, {{{highlight_green(matrix(1,7, Number, of, pens, "bought:", 40(3), "=", 120))}}}

  
                                                         Number of pencils bought: {{{matrix(1,3, (1/6) * 120, "=", 20)}}}
                                                        {{{highlight_green(matrix(1,7, Number, of, markers, "bought:", (2/5) * 20, "=", 8))}}}


As seen, 20 pencils were purchased for $50, so each pencil cost: {{{matrix(1,3, 50/20, "=", "$2.50")}}}
Therefore, $175 could buy {{{highlight_green(matrix(1,4, 175/2.5, "=", 70, pencils))}}}</pre>