PROBLEM SOLVING WITH EQUATIONS WORKSHEET

Problem 1 :

Jason and Mary are running on a 200 meter track. The expressions in the table above show the distance to the finish line t seconds after they started the race. How many meters will Mary have left to finish the race when Jason is on the finish line?

(A)  10.5 meters

(B)  11.5 meters

(C)  12.5 meters

(D)  13.5 meters

Problem 2 :

At a bagel shop the first 6 bagels purchased cost 55 cents a piece, and additional bagels cost c cents apiece. If a customer paid $5.70 for 12 bagels, what is the value of c?

(A)  25

(B)  30

(C)  35

(D)  40

Problem 3 :

Manny bought c candies at a price of 70 cents each. He sold all but k candies at a price of $1.25 each, and made a profit of p dollars. Which of the following represents p in terms of c and k?

(A)  p = 1.25(c - k) - 0.7c

(B)  p = 1.25c - 0.7c

(C)  p = 1.25c - 0.7(c - k)

(D)  p = 1.25(c - k) - 0.7k

Problem 4 :

David used ⅒ of his monthly salary for groceries and ⅙ of his remaining money for his car payment. He also paid twice as much money for rent as for his car payment. If David has $1620 left after paying for groceries, car payment, and rent, how much is his monthly salary?

(A)  $3240

(B)  $3320

(C)  $3480

(D)  $3600

Problem 5 :

In a school election, 680 students voted for one of two candidates for president. If the winner received 120 more votes than the loser, how many votes did the winner receive?

Problem 6 :

If a gas tank contains 15 liters of gas and is ⅜ full. How many additional liters of gas are needed to fill up the tank?

Answers

1. Answer :

When Jason is on the finish line,

-8t + 200 = 0

-8t = -200

t = 25

To find the distance Mary has left to finish the race when Jason is on the finish line, substitute t = 25 in the expression -7.5t + 200.

= -7.5(25) + 200

= -187.5 + 200

= 12.5 meters

Therefore the correct answer is option (C).

2. Answer :

The total for 12 bagels is $5.70.

Out of 12 bagels, first 6 bagels cost 55 cents each and the remaning 6 bagels cost c cents each.

6 ⋅ 0.55 + 6c = 5.70

3.30 + 6c = 5.70

6c = 2.4

c = $0.4

c = 40 cents

Therefore the correct answer is option (D).

3. Answer :

Each candy bought for 70 cents or $0.70.

Buying cost of c candies :

= 0.7c

Each candy sold for $1.25.

Number of candies sold = c - k.

Money received by selling (c - k) candies :

= 1.25(c - k)

Profit :

p = money received by sales - buying cost

p = 1.25(c - k) - 0.7c

Therefore the correct answer is option (A).

4. Answer :

Let x be David's monthly salary.

Money spent for groceries :

= (⅒)x

After having spent for groceries, remaning money :

= (⁹⁄₁₀)x

Money spent for car payment :

= (⅙)(⁹⁄₁₀)x

= (³⁄₂₀)x

Money spent for rent :

= two times of the money spent for car payment

= 2 ⋅ (³⁄₂₀)x

= (³⁄₁₀)x

Total money spent :

= (⅒)x + (³⁄₂₀)x + (³⁄₁₀)x

= (²⁄₂₀)x + (³⁄₂₀)x + (⁶⁄₂₀)x

= (¹¹⁄₂₀)x

After having spent for groceries, car payment and rent, the remaning money :

= (⁹⁄₂₀)x

Given : David has $1620 left after paying for groceries, car payment, and rent.

(⁹⁄₂₀)x = 1620

9x = 20 ⋅ 1620

x = 3600

David's monthly salary is $3600.

Therefore the correct answer is option (D).

5. Answer :

Let x be the number votes received by the winner.

Then the number votes received by the loser is (x - 120).

Total number of votes = 680.

x + (x - 120) = 680

x + x - 120 = 680

2x - 120 = 680

2x = 800

x = 400

Therefore, the winner received 400 votes.

6. Answer :

Let x be the total capacity of the tank in liters.

Given : The gas tank contains 15 liters of gas and is ⅜ full.

(⅜)x = 15

3x = 120

x = 40

Total capcity of the gas tank is 40 liters.

The tank already contains 15 liters of gas.

Additional liters of gas are needed to fill up the tank :

= 40 - 15

= 25

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