SOLUTION: squares, circles and pentagons in the ratio 3:4:1 respectively. The shapes are either made of wood or plastic. The ratio of wood squares to plastic squares is 3:2. 25% of the c

Question 1173955: squares, circles and pentagons in the ratio 3:4:1 respectively.
The shapes are either made of wood or plastic.
The ratio of wood squares to plastic squares is 3:2.
25% of the circles are wood.
2/3 of the pentagons are wood.
If there are 27 wood squares, how many plastic shapes are there?

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Let's label each sentence as fact 1 through fact 6

Fact 1) squares, circles and pentagons in the ratio 3:4:1 respectively.
Fact 2) The shapes are either made of wood or plastic.
Fact 3) The ratio of wood squares to plastic squares is 3:2.
Fact 4) 25% of the circles are wood.
Fact 5) 2/3 of the pentagons are wood.
Fact 6) There are 27 wood squares

From fact 3 and fact 6, we can say
(27 wood squares)/(x plastic squares) = 3/2
27/x = 3/2
27*2 = x*3
54 = 3x
3x = 54
x = 54/3
x = 18
There are 18 plastic squares.
Let A = 18 since we'll use it later.
There are 27+18 = 45 squares overall.

Let y be some positive whole number.
The ratio 3:4:1 is equivalent to 3y:4y:1y when we multiply both parts by y.

This new ratio says that we have 3y squares, 4y circles, and 1y pentagons. Earlier we found that we have 45 squares.
So,
3y = 45
y = 45/3
y = 15

This y value leads to
3y = 3*15 = 45 squares
4y = 4*15 = 60 circles
1y = 1*15 = 15 pentagons
The ratio 45:60:15 reduces to 3:4:1 when you divide all three parts by the GCF 15.

25% of the circles are wood (fact 4), so
25% of (60 circles) = 0.25*60 = 15
We have 15 wood circles and 60-15 = 45 plastic circles.
Let B = 45 since we'll need it later.

Earlier we found there are 15 pentagons. Two-thirds of those pentagons are wood (fact 5), which means (2/3)*15 = 10 pentagons are wood and 15-10 = 5 pentagons are plastic.
Let C = 5.

The values of A,B,C were aimed to collect all the plastic shape counts
A+B+C = 18+45+5 = 68

There are 68 plastic shapes

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Answer: 68

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