**Solving word problems with systems of equations worksheet :**

Worksheet given in this section will be much useful to the students who would like to practice solving word problems using system of linear equations.

1. A park charges $10 for adults and $5 for kids. How many many adults tickets and kids tickets were sold, if a total of 548 tickets were sold for a total of $3750 ?

2. Hertz Car Rental rents cars for x dollars per day plus y dollars for each mile driven. John rented a car for 4 days, drove it 160 miles, and spent $120. David rented a car for 1 day, drove it 240 miles, and spent $80. Write equations to represent John expenses and David expenses. Then solve the system and tell what each number represents.

**Problem 1 :**

A park charges $10 for adults and $5 for kids. How many many adults tickets and kids tickets were sold, if a total of 548 tickets were sold for a total of $3750 ?

**Solution : **

**Step 1 :**

Let "x" be the number of adults tickets and "y" be the number of kids tickets.

No. of adults tickets + No. of kids tickets = Total

x + y = 548 -------- (2)

**Step 2 : **

Write an equation which represents the total cost.

Cost of "x" no. adults tickets = 10x

Cost of "y" no. of kids tickets = 5y

Total cost = $3750

Then, we have

10x + 5y = 3750

Divide both sides by 5.

2x + y = 750 -------- (2)

**Step 3 :**

Solve an equation for one variable.

Select one of the equation, say x + y = 548.

Solve for the variable y in terms of x.

Subtract x from both sides.

(x + y) - x = (548) - x

y = 548 - x

**Step 4 : **

Substitute the expression for y in the other equation and solve.

2x + y = 750

2x + (548 - x)** ** = 750

Combine like terms.

x + 548 = 750

Subtract 548 from both sides.

x = 202

**Step 5 : **

Substitute the value of x we got above (x = 202) into one of the equations and solve for the other variable, y.

x + y = 548

202 + y = 548

Subtract 202 from both sides.

y = 346

So, the solution of the system is (202, 346).

**Step 6 : **

Interpret the solution in the original context.

Hence, the number of adults tickets sold is 202 and the number of kids tickets sold is 346.

**Problem 2 :**

Hertz Car Rental rents cars for x dollars per day plus y dollars for each mile driven. John rented a car for 4 days, drove it 160 miles, and spent $120. David rented a car for 1 day, drove it 240 miles, and spent $80. Write equations to represent John expenses and David expenses. Then solve the system and tell what each number represents.

**Solution : **

**Step 1 :**

John rented a car for 4 days, drove it 160 miles, and spent $120.

So, we have

4x + 160y = 120

**Step 2 :**

David rented a car for 1 day, drove it 240 miles, and spent $80.

So, we have

x + 240y = 80

**Step 3 :**

Solve an equation for one variable.

Select one of the equation, say x + 240y = 80.

Solve for the variable x in terms of y.

Subtract 240y from both sides.

(x + 240y) - 240y = (80) - 240y

x = 80 - 240y

**Step 4 : **

Substitute the expression for x in the other equation and solve.

4(80 - 240y) + 160y = 120

320 - 960y + 160y** ** = 120

Combine like terms.

320 - 800y = 120

Subtract 320 from both sides.

-800y = -200

Divide both sides by -800

(-800y)/(-800) = (-200)/(-800)

y = 0.25

**Step 5 : **

Substitute the value of y we got above (y = 0.25) into one of the equations and solve for the other variable, y.

x + y = 548

202 + y = 548

Subtract 202 from both sides.

x + 240y = 80

x + 240(0.25) = 80

x + 60 = 80

Subtract 60 from both sides.

x = 20

So, the solution of the system is (20, 0.25).

**Step 6 : **

Interpret the solution in the original context.

Hence, Hertz Car Rental rents cars for $20 per day plus $0.25 for each mile driven.

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