We create a conversion ratio that causes yards to cancel out, leaving only cents in the numerator and quilts in the denominator. This ratio is ((c cent )/(10 yard))((1 yard)/(q quilt))=(c )/(10q ) cent⁄quilt . Since the ratio has cents in the numerator and quilts in the denominator, it represents the price in cents per quilt.

1/3 of sales from cupcakes = $20, ¼ of sales from cream pies = $15 and the rest are from brownies = $60-$20-$15 = $25. Since each brownie costs 25 cents, Susan will have sold 100 of them.

Consider

(Bill + 7) = 2 x (Amy + 7)

(Amy – 2) = 1.5 x (Molly – 2)

Solve for Molly using the two equations by finding Amy’s age in terms of Molly’s age.

Amy = 2 + 1.5 Molly – 3 = 1.5 x Molly – 1

Substitute this into the first equation:

(Bill + 7) = 2 x (Amy + 7) = 2 x (1.5 x Molly – 1 + 7) = 2 x (1.5 x Molly + 6) = 3 x Molly + 12

Solve for Molly:

Bill + 7 – 12 = 3 x Molly

Molly = (Bill – 5) ¸ 3

Substitute Bill = 29

Molly = (Bill – 5) ¸ 3 = 8

Let original white chocolate pieces = W and original milk chocolate pieces = M. So the total number of pieces in the original bag is M + W.

From the first sentence: (M + W) x 0.2 = W or

0.2 M = 0.8 W or [M = 4W]

Once Christina has eaten 10 milk chocolate pieces, there are W pieces of white chocolate, (M – 10) pieces of milk chocolate and (M + W – 10) pieces total. According to the second sentence:

W ¸ (M – 10) = 3 ¸ 2

Or 2W = 3M - 30

Insert the equation in brackets: 2W = 3[4W] + 30 = 12W – 30

10W = 30 or W = 3 and M = 12

We want “How many pieces of chocolate are left in the bag” or (M – W – 10).

So (M +W – 10) = 3 + 12 – 10 = 5 

Cost = ( Miles driven / Miles per gallon) * 3.50

Total Mileage = City Miles + Highway Miles

30,000 = 10,000 + Highway Miles

Highway Miles = 20,000

Cost City = ( 10,000 miles / 33 miles per gallon ) * 3.50

Cost City = 303.03 * $3.50 = $1060.60

Cost Highway = ( 20,000 miles / 39 miles per gallon ) * 3.50

Cost Highway = 512.82 * $3.50 = $1794.87

Total Cost = Cost City + Cost Highway = $1060.60 + $1794.87 = $2855.47

If 20 students are girls, this is 2/3 of the class, giving 30 students total with 10 of them being boys. 4/5 of the boys will be 14, leaving 1/5 of the boys age 13. 1/5 of 10 is 2. 

Note that it is not necessary to find the solution to this problem. Thus, find an expression for x and an expression for y at their maximums and compare.

First, observe from the equation that x gets smaller as y gets bigger and y gets smaller as y gets bigger. This can be found by making the equation in the form (y = mx + b) and finding that m is negative. Thus there is a negative correlation between x and y.

Therefore at its maximum, x is such that y = 0. In other words, 

  x = 176,500 / 12

y is maximum when x = 0. In other words, 

  y = 176,500 / 3

Note that 176,500 / 3 > 176,500 / 12 because the denominator is smaller. 

The problem gives us two conversion ratios, which are (10¹⁸ meters/ 1 exameter) and (1 petameter/ 10¹⁵ meters).

We convert 1 exameter into petameters by multiplying 1 exameter by the conversion ratios so that all units other than petameters cancel out: 1 exameter * (10¹⁸ meters/ 1 exameter) * (1 petameter/ 10¹⁵ meters). Therefore one exameter is 10¹⁸_/10¹⁵  petameters. Finally, when dividing terms with common bases, we subtract the exponents, so our result is 10¹⁸_/10¹⁵ = 10³ = 1000.

The question is about similar triangles. The height of the two objects would correspond with each other and the shadows would correspond with each other. As with many geometry problems, it is helpful if you draw a diagram.  Set up a proportion for each so the height of Shaquille O'Neal to the height of the house then his shadow to the shadow of the house.

7/49 = 5/x

Solve for x by cross-multiplying:

5 * 49 = 7x

x = 35

If John is 35, that means currently Jack is 55 and Bob is 30.  55 – 30 = 25 years old when Bob was born.