Andrew has 14 coins consisting of nickels, dimes, and quarters. She has the same amount of dimes as quarters. How many of each coin does she have if the value of the coins is $2.20?

The sum of three different numbers is 108. The largest number is 60 more than the smallest number. The sum of the largest number and the smallest number is 36 more than twice the middle number. What is the largest of these numbers?

What is the solution to the following system of equations?

−x − 5y − 5z = 2

4x − 5y + 4z = 19

x + 5y − z = −20

(Hint: Wolfram Alpha Link in 3.4)

What is the value of z in the solution to the following system of equations?

−4x − 5y − z = 18

−2x − 5y − 2z = 12

−2x + 5y + 2z = 4

The following system of equations can be used to find the amount of money, in dollars, invested in three savings accounts. Write the matrix equation that represents this system of linear equations?

x + y + z = 9000

x − y − z = 0

.04x + .06y + .08z = 600

Ryan deposited less than $2,000 into two accounts. One account paid 4.5% and the other account paid 3% annual interest. After 1 year, he earned at least $40 in interest from the two combined accounts. If x represents the amount of money Ryan deposited at 4.5% and y represents the amount of money he deposited at 3%, write a system of inequalities that can be used to find the values of x and y?

This summer Piper’s town will be hosting a series of 15 concerts. There are two types of seats at the concerts, which are priced at $49.50 and $73.00. Piper would like to attend at least 8 concerts and spend no more than $500. If x and y represent the number of tickets Piper purchased for the 2 types of seats, Write the system of inequalities Piper could use to model this situation.

Cashews and peanuts are combined to make a nut mixture. At least ½ of the mixture, by weight, is cashews, and the total weight of the mixture cannot exceed 52 ounces. Write a system of inequalities that models this situation, where c represents the number of ounces of cashews and p represents the number of ounces of peanuts?

Harry needs to buy hamburgers and hot dogs for a picnic. He has only $82.00 to spend and must buy AT LEAST 98 hamburgers or hot dogs. A store charges $1.00 per hamburger and $0.50 per hot dog. Which of the following is a possible way Harry might buy hamburgers and hot dogs?

Which of these points is a solution to the system of inequalities below.

3x + 2y < 15

7x − 4y > 9

The graph of a system of linear inequalities is shown. What are the constraints to the system of linear equations?

A system of linear inequalities is below.

3x + 2y < 15

7x − 4y > 9

Which point is NOT a solution to this system?

Two customers each bought sets of tables and chairs from a furniture store offering a single price for chairs and a single price for tables. The amount paid by each customer is represented by the following inequalities, where c is the price of a single chair and t is the price of a single table.

8c + 4t > 250

4c + 2t < 250

Which could be the prices for a single chair and a single table?

Three linear inequalities form a system.

y > -6

y < x

y < -x

Which coordinate point is a possible solution to the system?