Question 1172306
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Let's break up the problem into these known facts:<ul><li>Fact 1: Bob spent 50 dollars on pens and markers. </li><li>Fact 2: The ratio of money spent on pens pencils and markers was 4:5:1. </li><li>Fact 3: Pens were sold at 3 for a dollar. </li><li>Fact 4: The number of pencils he bought was 1/6 of the number of pens. </li><li>Fact 5: The number of markers he bought was 2/5 of the number of pencils.</li></ul>Let x be some positive real number.
Fact 2 says the ratio of money spent on pens, pencils and markers is 4:5:1. 
This means 
4x dollars spent on pens
5x dollars spent on pencils
1x dollars spent on markers
The ratio 4x:5x:1x reduces to 4:5:1


So we have
4x+1x = 5x dollars
spent on pens and markers.


From fact 1, we know this figure is 50 dollars. So,
5x = 50
5x/5 = 50/5
x = 10


With this x value, we find that:
4x = 4*10 = 40 dollars spent on pens
5x = 5*10 = 50 dollars spent on pencils
1x = 1*10 = 10 dollars spent on markers


40+50+10 = 100 dollars was spent overall


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Pens were sold at 3 for a dollar (fact 3)


We can form these series of equations
3 pens = 1 dollar
6 pens = 2 dollars
9 pens = 3 dollars
12 pens = 4 dollars
And so on


The left side is triple that of the right side. 


In general we have 
3y pens = y dollars
where y is some nonnegative real number
We'll further say
y = amount of money spent on pens


Whatever dollar amount (y) you spent on pens, the number of pens you get is triple of that (3y)
So p = 3y where p is the number of pens


In the previous section, we found that $40 was spent on pens.
Use y = 40 to find p
p = 3y
p = 3*40
p = 120


So 120 pens were purchased.


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Earlier we defined p as the number of pens. 
Let's make c and m the number of pencils and markers. 


In other words,
p = number of pens
c = number of pencils
m = number of markers
all of these values are nonnegative whole numbers


From fact 4, we know that,
c = (1/6)*p
c = p/6
c = 120/6 ... plug in p = 120
c = 20
Bob purchased 20 pencils


And from fact 5, we can say,
m = (2/5)*c
m = (2/5)*20 ... plug in c = 20
m = 0.4*20
m = 8
He also bought 8 markers


We have this summary
120 pens purchased
20 pencils purchased
8 markers purchased


This shows he bought 120+8 = 128 pens and markers


That wraps up the first question.

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Now onto the second question.


Recall earlier that $100 was spent overall. 
Let's bump this up to $175


The ratio 4x:5x:1x would then lead us to
4x+5x+1x = 175
10x = 175
x = 175/10
x = 17.5


This means
4x = 4*17.5 = 70 
dollars is spent on pens


Then y = 70 leads to
p = 3y
p = 3*70
p = 210
210 pens were purchased


And,
c = p/6
c = 210/6
c = 35
35 pencils were purchased


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Final Summary:


Question: How many pens and markers did he buy?
<font color=red>Answer: 128</font>


Question: How many pencils could he buy for 175 dollars?
<font color=red>Answer: 35</font>
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