8th Grade Math Lesson 2-6 practice problems
Write an equation and solve it. Show all work.
1. Will had two less than three times as many video games as Josh.
If Will has 20, how many does Josh have?
2. Kayla purchased 5 large sodas at the movie theater. Before tax was added, the total cost of the 5 sodas was equal to the cost of 3 sodas plus $7. What was the cost of one soda?
3. Katherine works flexible hours. This month she worked a total of 60 hours, which was 3 more than 5 times as many hours as she worked last month. How many hours did she work last month?
4. Matt is saving for college. He puts $20 in his savings account each week. How many weeks will it take for him to save $15,000?
5. A cell phone company charges a shipping fee of 7% of the purchase cost, p. If the total cost of shipping is calculated to be $30.25, what is the purchase price before shipping was added?
1. Let's represent the number of video games Josh has with the variable "J".
The number of video games Will has is 3 times as many as Josh's, minus 2. So we can write the equation as:
Will's video games = 3J - 2
Since Will has 20 video games, we can substitute that into the equation:
20 = 3J - 2
To solve the equation, we can add 2 to both sides:
20 + 2 = 3J
22 = 3J
Finally, we divide both sides by 3 to solve for J:
22/3 = J
J ≈ 7.33
Therefore, Josh has around 7.33 video games.
2. Let's represent the cost of one soda with the variable "S".
The total cost of 5 sodas is equal to the cost of 3 sodas plus $7. We can write the equation as:
5S = 3S + 7
To solve the equation, we can subtract 3S from both sides:
5S - 3S = 7
2S = 7
Finally, we divide both sides by 2 to solve for S:
2S/2 = 7/2
S ≈ 3.50
Therefore, the cost of one soda is around $3.50.
3. Let's represent the number of hours Katherine worked last month with the variable "L".
The total number of hours Katherine worked this month is equal to 5 times the number of hours she worked last month, plus 3. We can write the equation as:
60 = 5L + 3
To solve the equation, we can subtract 3 from both sides:
60 - 3 = 5L
57 = 5L
Finally, we divide both sides by 5 to solve for L:
57/5 = L
L ≈ 11.40
Therefore, Katherine worked around 11.40 hours last month.
4. Let's represent the number of weeks it will take for Matt to save $15,000 with the variable "W".
Matt saves $20 each week, so the total amount saved in W weeks is equal to $20 times W. We can write the equation as:
20W = 15000
To solve the equation, we divide both sides by 20:
20W/20 = 15000/20
W = 750
Therefore, it will take Matt 750 weeks to save $15,000.
5. Let's represent the purchase cost before shipping with the variable "P".
The shipping fee is 7% of the purchase cost, so we can write the equation as:
0.07P = 30.25
To solve the equation, we divide both sides by 0.07:
0.07P/0.07 = 30.25/0.07
P = 432.14
Therefore, the purchase price before shipping was added is $432.14.
1. Let's start by writing an equation based on the information given.
If Will has 20 video games and he has two less than three times as many as Josh, we can represent Josh's number of video games as J.
The equation would be: 20 = 3J - 2
To solve for J, we need to isolate J on one side of the equation.
Adding 2 to both sides of the equation, we get: 20 + 2 = 3J
Simplifying, we have: 22 = 3J
Finally, dividing both sides by 3, we find: J = 22/3
So Josh has approximately 7.33 (or 7 and 1/3) video games.
2. Let's represent the cost of one soda as x.
According to the information given, the total cost of 5 large sodas is equal to the cost of 3 sodas plus $7.
We can write this as an equation: 5x = 3x + 7
To solve for x, we need to isolate x on one side of the equation.
Subtracting 3x from both sides of the equation, we get: 5x - 3x = 7
Simplifying, we have: 2x = 7
Finally, dividing both sides by 2, we find: x = 7/2
So the cost of one soda is $3.50.
3. Let's represent the number of hours Katherine worked last month as x.
According to the information given, the total number of hours Katherine worked this month, which is 60, is equal to 3 more than 5 times the number of hours she worked last month.
We can write this as an equation: 60 = 5x + 3
To solve for x, we need to isolate x on one side of the equation.
Subtracting 3 from both sides of the equation, we get: 60 - 3 = 5x
Simplifying, we have: 57 = 5x
Finally, dividing both sides by 5, we find: x = 57/5
So Katherine worked approximately 11.4 (or 11 and 2/5) hours last month.
4. Let's represent the number of weeks Matt saves as w.
According to the information given, Matt puts $20 in his savings account each week, and he wants to save $15,000.
We can write this as an equation: 20w = 15000
To solve for w, we need to isolate w on one side of the equation.
Dividing both sides by 20, we get: w = 15000/20
Simplifying, we have: w = 750
So it will take Matt approximately 750 weeks to save $15,000.
5. Let's represent the purchase cost before shipping as p.
According to the information given, the shipping fee is 7% of the purchase cost and the total cost of shipping is $30.25.
We can write this as an equation: 0.07p = 30.25
To solve for p, we need to isolate p on one side of the equation.
Dividing both sides by 0.07, we get: p = 30.25/0.07
Simplifying, we have: p = 432.14
So the purchase price before shipping was added is approximately $432.14.