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.

We have here a basic ratio:

6/24 = 57/x

Solving for x, we get: 6x = 24 * 57; 6x = 1368; x = 228

Now, we must be very careful here, however. Is 228 an even multiple of 24?  228/24 = 9.5.  That means that we would have to do 9.5 batches.  The question indicates that these are batched in groups of 6; therefore, we have to run 10 batches to get our amount. That would be 240 minutes or 4 hours.

Set up a proportion and conver 4 hours and 20 minutes into just minutes for now,

so 26/260 = 100/X

Solve for X = 1000 minutes

1000/60 = 16 hours and 40 minutes

We can set up a ratio of  and then solve for . 

The weight will be 150 grams + (1.15 – 0.55)/0.05 * 50g.

You need to subtract first 150 grams cost from the total cost and divide by the price per unit to determine how many units. Next, multiply units by weight per unit and add to the original first 150 grams.

 150 + 600 = 750 grams

This is the maximum weight that can be sent at that price; the minimum weight that could be charged this price would be 701 grams. Hence a package weighing 750 grams will be charged $1.15.