In a football tournament, the Bees scored 9 less than three times as many points as the Hornets. The Wasps scored 28 more points than the Hornets. Together the three teams scored 184 points. Let x represent the number of points scored by the Hornets. Complete the steps to solve the equation (3x – 9) + x + (x + 28) = 184. Then answer the question. 1. Combine like terms. 2. Use the subtraction property of equality. 3. Use the division property of equality. 4. Use the variable to answer the question. How many points did the Bees score? points

Since, it is said that x respresents the number of points scored by the Hornets, that is your variable and all the verbal statements will be translated using x:

a) NUmber of points scored by the Hornets: x

b) The Bees scored 9 less than three times as many points as the Hornets ⇒v3x - 9

c) The Wasps scored 28 more points than the Hornets ⇒ x + 8

d) Together the three teams scored 184 points ⇒

x + (3x - 9) + (x + 28) = 184

Which indeed is the given equation: (3x – 9) + x + (x + 28) = 184

Now, complete the steps to show it, in the same order given:

1. Combine like terms.

Remove the parenthesis: x + 3x - 9 + x + 28 = 184

Combine the terms on x on the left: x + 3x + x = 5x

Combine the constants on the left: - 9 + 28 = 19

Write the result: 5x + 19 = 184

2. Use the subtraction property of equality.

Subtract 19 from both sides: 5x + 19 - 19 = 184 - 19

Due the operations: 5x = 165

3. Use the division property of equality. 4.

Divide both sides by 5: (5x / 5) = 165 / 5

Due the operations: x = 33

4. Use the variable to answer the question. How many points did the Bees score?

The expression for the points scored by the Bees is 3x - 9, so substitute x in that expression: 3 (33) - 9 = 99 - 9 = 90.

Answer: the Bees scored 90 points.

johanrusli johanrusli · Answer 2 · 2019-11-19T09:05:46+01:00

The Bees scored 90 points

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Further explanation

Simultaneous Linear Equations could be solved by using several methods such as :

Elimination Method
Substitution Method
Graph Method

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

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Let:

The number of points scored by the Hornets = x

The number of points scored by the Bees = y

The number of points scored by the Wasps = z

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The Bees scored 9 less than three times as many points as the Hornets.

[tex]y = 3x - 9[/tex]

The Wasps scored 28 more points than the Hornets.

[tex]z = x + 28[/tex]

Together the three teams scored 184 points.

[tex]y + x + z = 184[/tex]

[tex](3x - 9) + x + (x + 28) = 184[/tex]

[tex]3x + x + x - 9 + 28 = 184[/tex] → 1. Combine like terms

[tex]5x - 9 + 28 = 184[/tex]

[tex]5x + 19 = 184[/tex]

[tex]5x + 19 - 19 = 184 - 19[/tex] → 2. Use the subtraction property of equality

[tex]5x = 165[/tex]

[tex]5x \div 5= 165 \div 5[/tex] → 3. Use the division property of equality

[tex]x = 33[/tex]

[tex]\texttt{ }[/tex]

[tex]y = 3x - 9[/tex]

[tex]y = 3(33) - 9[/tex] → 4. Use the variable to answer the question

[tex]y = 99 - 9[/tex]

[tex]y = 90[/tex]

[tex]\texttt{ }[/tex]

Learn more

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations