Envision Math 2.0: Grade 8, Volume 1
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2. Solve Equations with Variables on Both Sides
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Exercise 10 Page 95

Mark the number of hours with snowfall as x. Describe the snowfalls in both towns in terms of x to make an equation.

45

Practice makes perfect
We are told that two towns have accumulated different amounts of snow. In Town 1 there is already 5 inches of snow and its depth is increasing by 3 12 inches every hour. In Town 2 there is 6 inches and the depth is increasing by 2 14 inches every hour. We want to find the number of hours after which the snowfalls in two towns will be equal. Let's start with defining x. x - the number of hours with snowfall Let's now express the snowfalls of both towns in terms of x. In Town 1 there is 3 12 inches of snow every hour plus 5 inches. Therefore, the snowfall will be the number of hours x multiplied by 3 12 plus 5. In Town 2 there is 2 14 inch of snow every hour plus 6 inches, so the snowfall will be the number of hours x multiplied by 2 14 plus 6. Snowfall in Town A:& 3 12x+ 5 Snowfall in Town B:& 2 14x+ 6 We want the snowfalls to be equal, so we need to make an equation that will have the snowfall of Town 1 on the left-hand side and the snowfall of Town 2 on the right-hand side. 3 12x+ 5 = 2 14x+ 6 Now we will solve the obtained equation. We will use the inverse operations to combine like terms on both sides of the equals sign and solve for x.
3 12x+5 = 2 14x+6
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Solve for x
3 12x- 2 14x+5 = 2 14x- 2 14x+6
3 12x-2 14x+5 = 6
3 12x-2 14x+5- 5 = 6- 5
3 12x-2 14x=1
7/2x-9/4x=1
14/4x-9/4x=1
5/4x=1
5/4x* 4/5=1* 4/5
20/20x=4/5
x=4/5
The snow will have to fall for 45 hours for the snowfall to be equal in both towns.