These questions are just a matter of extracting the information and putting it into an algebraic equation.

1A)

Your data set contains 5 numbers: {91, 86, 73, 79, and x}

x = the score on the last test.

We want this equation to equal 400, the minimum number of points to receive a B.

91 + 86 + 73 + 79 + x = 400

So we sum up the numbers that we can and isolate the x on one side of the equation to solve for x.

329 + x = 400

-329 -329

x = 71

The student must make a score of 71 on the last Chemistry test to receive a B.

2A)

We know the person has to be spend $13.95 for that day PLUS 10 cents per mile --> 10c/mile

So,

13.95 + .10x <---where x = the number of miles accrued on that day.

Our daily budget is $76. So the person cannot spend more than this amount on any given day.

Therefore our equation is:

13.95 + .10x = 76

Then we solve for x by isolate the x on one side of the equation:

13.95 + .10x = 76

-13.95 -13.95

.10x = 62.05

We divide by .10 to get the x by itself,

.10x = 62.05

.10 .10

x = 620.5

So the answer is 620.5 miles or less to stay within budget.

3A)

Commonsense tells us that the part we invest at 12%( we'll call this part x), will be less than the part that we invest at 16% (we'll call this part y).

Therefore x < y.

We also know that,

x + y = 20,000 and,

.12x + .16y = 3,000

This can be solved 2 different ways.

1) Substitution or

2) By canceling out one variable and solving for the other variable.

I will be solving by substitution:

Since the question asks us what can be the most invested at 12%, we will be solving for x.

So we want to find our y in terms of x.

x + y = 20,000

-x -x

y = 20,000 - x

Then we just input this equation 20,000 - x in place of y in the second equation.

.12x + .16y = 3,000

.12x + .16(2,000 - x) = 3,000

.12x + (.16*20,000) - (.16*x) = 3,000

.12x + 3,200 - .16x = 3,000

3,200 - .04x = 3,000

-3,200 -3,200

- .04x = -200

- .04 -.04 **Remember that when we divide negative numbers, we get a positive number **

x = 5,000

So at most, we will invest $5,000 at 12% in order to make at least $3,000 interest per year.