Answer:
- <u>The Bees scored 90 points.</u>
Explanation:
First, let's prove that the equation is correct.
To create the equation, you translate the verbal statements into algebraic expressions.
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:
<u>1. Combine like terms. </u>
- 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
<u>2. Use the subtraction property of equality. </u>
- Subtract 19 from both sides: 5x + 19 - 19 = 184 - 19
- Due the operations: 5x = 165
<u>3. Use the division property of equality. 4. </u>
- Divide both sides by 5: (5x / 5) = 165 / 5
- Due the operations: x = 33
<u>4. Use the variable to answer the question. How many points did the Bees score?</u>
- 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.
