Arthur D. answered • 10/22/14

Forty Year Educator: Classroom, Summer School, Substitute, Tutor

Kayla W.

asked • 10/22/14using 1 inch = 15 ft as the scale factor what are the blueprint demisions of a room in a model house that is actually 30ft x 45ft?

a bag contains 10 white golf balls and 6 striped golf balls. a glofer wants to add 112 golf ball to the bag . he wants the ratio of striped golf balls to remain the same how many of each should he add?

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Arthur D. answered • 10/22/14

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Seeing that you don't understand the solution to the second problem you can solve it with arithmetic because the numbers are small.

The ratio of white to striped is 10 to 6 which means for every 10 white balls there are 6 striped balls.

You want to add 112 balls.

white striped

10 6 16 total

20 12 32 total

30 18 48 total

40 24 64 total

50 30 80 total

60 36 96 total

70 42 112 total (all done)

Byron S. answered • 10/22/14

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Math and Science Tutor with an Engineering Background

For the first problem, set up proportions:

1 inch / 15 ft = x inches / 30 ft

1 inch / 15 ft = y inches / 45 ft

You can cross multiply to solve.

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For the second problem, you have a ratio of 10:6 white:striped golf balls in groups of 10+6=16 golf balls.

112/16 = 7, so he needs to add 7 more groups. Each group has 10 white and 6 striped. How many are added total of each?

Byron S.

For the first problem, if you have two fractions that are equal, you can multiply the numerator (top) of each times the denominator (bottom) of the other, and they're still equal. In the first proportion I wrote, this comes out to:

1 * 30 = x * 15

30 in*ft = (15 ft)(x in)

Divide both sides by 15 ft, and you find

2 in = x

You can do the same thing for the 45 ft dimension.

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10/22/14

Byron S.

For the second one, the bag starts with 10 white and 6 striped balls. The easiest way to keep the ratio the same is to keep adding exactly the same number of each type of ball repeatedly. Arthur approached this by simply adding another 10 and 6 until he got to the 116 that was added.

The approach I described earlier considers the 10 and 6 balls as a group of 16 total. If you keep adding copies of these 16 balls repeatedly, you'll keep the ratio the same, and you need to do it until you get 16*7 = 116 balls added. That means you're adding 10*7=70 white balls and 6*7=42 striped balls. As you can see, both give the same result. Hopefully you understand at least one of these two methods!

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10/22/14

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Kayla W.

10/22/14