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.

The question says that the mixture has 5 units of flour for every 1 unit of sugar, which adds up to a total of 5 + 1 = 6 units of the mixture; therefore in 6 kilograms of the mixture, 1 kilogram will be sugar.

To find how much sugar will be in 12 kilograms of the mixture, we multiply the amount of sugar in 6 kilograms of the mixture by 2, giving us 1 kilogram of sugar * 2 = 2 kilograms of sugar.

The best estimate would be to simply divide the number of printers by the number of offices. However, they only gave us the average number of employees per office, thus to find the number of offices we divide:

14,000 (people)/12.5 (per office) = 14,000/12.5 = 1,120 offices

We already know the number of printers available total, thus again divide

3,400 (printers)/1,120 (offices) = 3.04, or 3.0 printers per office as the best estimate.