Name _____________________________________________________ Date ______________ Hour __________

D-08 Systems of Equations Word Problems

We discussed how to write equations in standard form to help solve system of equations style word

problems. Remember that we had to look for all of the numbers in a problem and circle them- three

should have the same unit or relate to the same topics; there is usually one number that stands out

with a different unit.

A, B, and C in the standard form equation should all have the same unit/relate to the same topic- so

make sure you aren’t mixing up the two units/topics.

You can choose whether you want to solve with elimination or substitution. Some problems lend

themselves to one technique over the other, so we will practice determining which of the two

techniques is the better technique to use. I do not recommend graphing- the most mistakes are

made when students try to use graphing to solve a system of equations world problem (plus, we

typically get a lot of decimals in these word problems).

Directions: Write a system of equations to represent each word problem. Then, solve your system of

equations. It may be helpful to label each variable (typically x and y) with what they represent- that

way, when you add units to your answer, you know what the units should be!

1. Last year, you mowed grass and shoveled snow for 12 households. You earned $225 for mowing a

household’s lawn for the entire year and you earned $200 for shoveling a household’s driveway for

an entire year. You earned a total of $2,600 last year. How many households did you mow the lawn

for, and how many households did you shovel the driveway for?

2. You will be making hanging flower baskets. The plants you have picked out are blooming annuals

and non-blooming annuals. The blooming annuals cost $3.20 each and the non-blooming annuals

cost $1.50 each. You bought a total of 24 plants for $49.60. How many of each plant type did you

buy?

3. Two families go to a hockey game. One family purchased two adult tickets and four youth tickets

for $28. Another family purchased four adult tickets and five youth tickets for $45.50. How much does

an adult ticket cost? How much does a youth ticket cost?

4. Sarah has 600 quarters and dimes in her piggy bank, which totals to $123.75. How many quarters

and dimes does she have? (Hint: use cent values for quarters and dimes).