# Systems of Equations and Inequalities (Math Problem Sample)

SLP Assignment Expectations

Complete the following problems using the SLP 4 Answer Template.

Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.

Describe the three types of solutions systems of equations have when graphed.

The sum of two numbers is 30 and their difference is 2. Find the two numbers by writing and solving a system of equations.

Two apples and three pears cost $3.45. Three apples and five pears cost $5.55. Find the cost of each type of fruit.

Mary has a total of $5,000 invested in two accounts. One account pays 5% and the other 8%. Her interest in the first year was $331. Write and solve a system of equations to find out how much she has invested in both accounts.

Terry is mailing two boxes. Together they weigh 21 lbs. If the smaller box is 5 lbs. less than the larger one, how much does each box weigh? Write and solve an equation that models this scenario.

The length of a pool is 3 feet more than twice its width. If the perimeter of the pool is 72 feet, find the dimensions of the pool by writing and solving a system of equations.

A desk and a chair cost $200 as a set. If the desk costs four times more than the chair, how much does each one cost? Write and solve using a system of equations.

Rachel has 15 coins with a value of $2.85. If the coins are either dimes or quarters, how many of each coin does she have? Write and solve using a system of equations.

A music concert was attended by 450 people. Adult tickets sold for $70 and children’s tickets for $40. If total sales were $27,750, how many of each ticket was sold?

A party planner can spend a maximum of $5,000 on food. If the chicken dinner (x) costs $20 and the steak dinner (y) costs $25, make a graph of the region that shows the possibilities for the number of chicken and steak dinners that can be purchased while still staying within budget. Shade the solution set.

source..MAT101 SLP 4 Answer Template

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Use this template to insert your answers for the assignment. Please use one of the four methods for showing Your work (EE, Math Type, ALT keys, or neatly typed). Remember that Your work should be clear and legible.

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Write the final answer in the terms being asked such as dollars/cents, degrees, tickets, etc.

1. Describe the three types of solutions systems of equations have when graphed.

Answer: __________________________________________________________

1 linear equations e.g. 2a+4b=30

These systems can have no solution, many solutions or a unique solution.

2 Unique solution equation e.g. (2,3,4) or A=2.B=3 ,C=4

The number of variables is equal to the number of non-zero rows.

3 Infinitely many solution-It is consistent and the number of variables is more than the number Of non-zero rows

e.g. (2a-2b+3c, 2a+3b-c, 7c)

2. The sum of two numbers is 30 and their difference is 2. Find the two numbers by writing and solving a system of equations.

Calculations:

Answer: _______________

Let the 2 numbers be A and B

A+B=30

A-B=2

Therefore by substitution

2A=32

A=16

B=14

3. Two apples and three pears cost $3.45. Three apples and five pears cost $5.55. Find the cost of each type of fruit.

Calculations:

Answer: _______________

A-Apples

P-pears

2A+3P=3.45

3A+5P=5.55

By substitution

2A=1.2

A=0.6

P=0.75

1 apple=0.6

1 pear=0.75

4. Mary has a total of $5000 invested in two accounts. One account pays 5% and the other 8%. Her interest in the first Bear was $331. Write and solve a system of equations to find out how much she has invested in both accounts.

Calculations:

Answer: _______________

Let 2 accounts be A and B

A+B=5000

0.05A+0.08B=331

By substitution

0.6B=1620

B=2700

A=2300

Therefore, amount invested in account A =$2,300

Amount invested in account B=$ 2,700

5. Terry is mailing two boxes. Together they weigh 21 lbs. If the smaller box is 5 lbs. less than the larger one, how much does each box weigh? Write and solve an equation that models this scenario.

Calculations:

Answer: _______________

Let the 2 boxes be A and B

A+B=21lbs

A-B=5lbs

BB substitution:

2B=16

B= 8lbs

A= 13lbs

Therefore,

Bigger box B=13 lbs

Smaller box A= 8lbs

6. The length of a pool is 3 feet more than twice its width. If the perimeter of the pool is 72 feet, find the dimensions of the pool by writing and solving a system of equations.

Calculations:

Answer: _______________

L=length

W=width

L-2W=3

2L+2W=72

By substitution

6W=66

W=11 feets

L=25 feets

Therefore,

Length=25 feets

Width=11 feets

7. A desk and a chair cost $200 as a set. If the desk costs four times more than the chair, how much does each one cost. Write and solve using a system of equations.

Calculations:

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