Quiz about System of Equations Word Problems

Question 1

Suppose you have 20 coins. If the coins are quarters and nickels only and are worth $2.60, which system of equations would represent this problem?

Let N = # of Nickels and let Q represent the # of Quarters

Accepted Answer

$$N+Q=20$$

$$N\left(.05\right)+Q\left(.25\right)=2.60$$

Answer

$$N\ +\ Q\ =\ 20$$

$$N\left(5\right)+Q\left(25\right)=2.60$$

Answer

$$N\ +\ Q\ =\ 20$$ $$N\ +\ Q\ =\ 2.60$$

Answer

$$N\left(.05\right)+Q\left(.25\right)=20$$ $$N\ \ +\ Q\ =\ 2.60$$

Question 2

A fruit basket containing only apples and pears is worth $9.00. Each apple costs $0.75 and each pear costs $0.50. What system would represent this problem if there are 14 pieces of fruit in all?

A = # apples and P = # of pears

Accepted Answer

$$A\ +P=14$$

$$A\left(.75\right)+P\left(.50\right)=9.00$$

Answer

$$A-P=14$$ $$75A-50P=9.00$$

Answer

$$A\ +\ P\ =\ 9.00$$ $$A\left(.75\right)+P\left(.50\right)=14$$

Answer

$$A+P=14$$

$$A+P=9.00$$

Question 3

A small theatre can only seat 72 people. A sold out play took in $407.50 in ticket sales. If adult tickets are $6.50 and student tickets are $3.75, how many adults and how many students attended?

Let A = # Adults and S = # Students,

Which equation system represents this problem?

Accepted Answer

$$A+S=72$$

$$A\left(6.50\right)+S\left(3.75\right)=407.50$$

Answer

$$A+S=72$$

$$A\left(3.75\right)+S\left(6.50\right)=407.50$$

Answer

Insufficient information to solve

Answer

$$A+S=407.50$$ $$A\left(6.50\right)+S\left(3.75\right)=72$$

Question 4

A chemist needs to create a 250 mL solution that contains 30% acid. If they have a 25% acid solution and a 75% acid solution, how many milliliters of each must be mixed to create the solution needed?

Which system can be used to solve this?

Let x = Amount of 25% acid and let y = Amount of 75% acid solutions

Accepted Answer

$$x\ +\ y\ =\ 250$$

$$.25x+.75y=.30\left(250\right)$$

Answer

$$x+y=250$$

$$.75x+.25y=250$$

Answer

$$.30x+.30y=.30\left(250\right)$$ $$x+y=250$$

Answer

$$25x+30y=260$$ $$x+y=.30\left(260\right)$$

Question 5

The sum of a two-digit number is 13. When you reverse the digits, you decrease the number by 45. Which system can be used to find the number?

Let the variables xy represent the two digit number (x in the tens place, y in the ones place)

Accepted Answer

$$x+y=13$$

$$10y+x=10x+y-45$$

Answer

$$10x+y=13$$

$$10x+y=45+10y+x$$

Answer

$$x+y=13$$

$$xy=yx-45$$

Question 6

A boat traveled from city A to city B and back. The cities are 200 miles apart. The trip downstream took 10 hours but the trip upstream took 20 hours. Which system would help us find the speed of the boat in still water (B) and also the speed of the current (C)?

Note: Distance = Rate (aka speed) x Time

Accepted Answer

$$200=\left(B+C\right)10$$

$$200=\left(B-C\right)20$$

Answer

Insufficent information to solve

Answer

$$200=B+C$$

$$200=B-C$$

Answer

$$200=B\left(10\right)+C\left(10\right)$$ $$200=B\left(20\right)+C\left(20\right)$$

System of Equations Word Problems

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