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
Found 3 solutions by math_tutor2020, MathTherapy, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Let's break up the problem into these known facts:- Fact 1: Bob spent 50 dollars on pens and markers.
- Fact 2: The ratio of money spent on pens pencils and markers was 4:5:1.
- Fact 3: Pens were sold at 3 for a dollar.
- Fact 4: The number of pencils he bought was 1/6 of the number of pens.
- Fact 5: The number of markers he bought was 2/5 of the number of pencils.
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
----------------------------------------
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.
-----------------------------------------
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.
-----------------------------------------
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
=================================================
Final Summary:
Question: How many pens and markers did he buy?
Answer: 128
Question: How many pencils could he buy for 175 dollars?
Answer: 35
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website! 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
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 
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, 
Number of pencils bought: 
As seen, 20 pencils were purchased for $50, so each pencil cost: 
Therefore, $175 could buy 
Answer by ikleyn(52903)  (Show Source):
You can put this solution on YOUR website! .
How this "problem" is worded, printed, written and presented, it is out of the human logic.
It is the same as to tell a tale story not from the beginning, but from the middle,
pretending that the beginning part does not exist, at all.
|
|
|
