# Lesson Worksheet: Applications on Systems of Linear Equations in Three Variables Mathematics • 9th Grade

In this worksheet, we will practice solving real-world problems using a system of linear equations in three variables.

Q1:

If the measure of one angle of a triangle is half the measure of the second angle and less than the measure of the third one by , then what are the measures of the three angles?

• A
• B
• C
• D

Q2:

Jackson, Daniel, and Jennifer each had 1 pound to spend in the candy shop. Jackson bought a packet of Stars and a bar of Coolies and got 13 pence in change. Daniel bought a packet of Stars and a Munch bar and got 17 pence in change. Jennifer bought a bar of Coolies and a Munch bar and got 40 pence in change. Their friend Hannah wanted to buy three packets of Stars, four bars of Coolies, and five Munch bars for her family. How much would it cost her?

Q3:

Sophia bought 3 plastic cars and 2 plastic boats for . Charlotte spent 4p less on 1 car, 1 boat, and 2 bikes. David got 2 boats and a bike for . How much does one plastic bike cost?

Q4:

If the dimensions of a rectangular prism are whole numbers such that , , and , what is its volume?

Q5:

A budget of pounds was set by the authorities for one of the villages to build a new school, a hospital, and a sports club. If the cost of the school is that of the hospital, and the cost of the hospital is that of the sports club, determine the cost of each of them.

• ASchool = , hospital = , sports club =
• BSchool = , hospital = , sports club =
• CSchool = , hospital = , sports club =
• DSchool = , hospital = , sports club =

Q6:

39,600 LE is to be shared between a woman, 2 boys and 5 girls. The woman will receive of the money. Each boy receives twice as much as each girl. How much money do the woman, each boy and each girl receive?

• AThe share of the woman is 4,950 LE, the share of a boy is 7,700 LE, and the share of a girl is 3,850 LE.
• BThe share of the woman is 4,950 LE, the share of a boy is 3,850 LE, and the share of a girl is 7,700 LE.
• CThe share of the woman is 4,950 LE, the share of a boy is 3,850 LE, and the share of a girl is 4,400 LE.
• DThe share of the woman is 4,950 LE, the share of a boy is 8,800 LE, and the share of a girl is 4,400 LE.
• EThe share of the woman is 4,950 LE, the share of a boy is 3,850 LE, and the share of a girl is 3,850 LE.

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