Caitlyn spends $17 at the store. She buys a mop for $5 and 3 bottles of floor cleaner. If x represents the cost of each bottle of cleaner, the equation that can be used to find the value of x is 3 x + 5 = 17. Which shows the first step that should be taken to verify that $4 is the solution to the equation?
3 (4) minus 5 = 17
3 (4) = 17 + 4
3 (4) + 5 = 17 + 5
3 (4) + 5 = 17
+ 3
be specific
The first step that should be taken to verify that $4 is the solution to the equation is: substitute $4 for x in the equation and simplify. So, it would be 3(4) + 5 = 17.
A two-day moving truck rental from Best Rentals costs $60 and $0.35 per mile driven. A two-day moving truck rental from Easy Movers costs $80 and $0.25 per mile driven. Let m represent the number of miles driven. Which equation can be used to find the number of miles for which the rentals would cost the same amount?
60 + 0.35 m = 80 + 0.25 m
60 m + 0.35 = 80 + 0.25 m
60 + 0.35 m = 80 m + 0.25 m
60 m + 0.35 = 80 m + 0.25
m
be sapecific
The equation that can be used to find the number of miles for which the rentals would cost the same amount is: 60 + 0.35m = 80 + 0.25m.
A regular hexagon and a rectangle have the same perimeter, P. A side of the hexagon is 4 less than the length, l, of the rectangle. The width of the rectangle, w, is 2 less than the length of the rectangle. What is the perimeter of the hexagon?
A rectangle with a length of l and width of w. P = 2 l + 2 w. A hexagon with side lengths of s. P = 6 s.
Since the rectangle and the hexagon have the same perimeter, we can set their formulas for perimeter equal to each other, and solve for the value of s (side length of the hexagon):
2l + 2w = 6s
We can also use the given information that a side of the hexagon is 4 less than the length of the rectangle, so:
s = l - 4
And the width of the rectangle is 2 less than the length, so:
w = l - 2
We can substitute these expressions for s and w into the first equation:
2l + 2(l - 2) = 6(l - 4)
Simplifying:
4l - 8 = 6l - 24
2l = 16
l = 8
Now we can use the expression for s to find the side length of the hexagon:
s = l - 4 = 4
Finally, we can use the formula for the perimeter of the hexagon to find its value:
P = 6s = 6(4) = 24
Therefore, the perimeter of the hexagon is 24.
Tomas bought 3 software apps and 2 e-books for a total of $21. The two e-books cost $12. If s represents the cost of each app, the total cost of all 5 items is represented by 3 s + 12 = 21. Which statement about verifying the solution for s is true?
The solution is given by s = 6 because it makes the value of 3 s + 12 equal to 21.
The solution is given by s = 3 because it makes the value of 3 s + 12 equal to 21.
The solution is given by s = 9 because it makes the value of 3 s + 12 equal to 21.
The solution is given by s = 12 because it makes the value of 3 s + 12 equal to 21.
The statement that is true about verifying the solution for s is:
The solution is given by s = 3 because it makes the value of 3s + 12 equal to 21.
To verify, we can substitute s = 3 into the equation 3s + 12 = 21:
3(3) + 12 = 21
9 + 12 = 21
21 = 21
Since the equation is true, we have verified that the solution s = 3 is valid.
Kyung works 5 hours at a restaurant each Wednesday. He also earns $37 a week delivering newspapers. Kyung makes a total of $79.50 each week. If m represents the amount he makes per hour at the restaurant, which equation can be used to find the value of m?
5 m + 37 = 79.50
5 m = 79.50
37 m = 79.50
37 m + 5 = 79.50
The equation that can be used to find the value of m is:
5m + 37 = 79.50
This is because the total amount Kyung makes each week is the sum of what he earns at the restaurant and what he earns delivering newspapers. The amount he makes at the restaurant is equal to his hourly rate (m) multiplied by the number of hours he works (5), so 5m represents his earnings from the restaurant. Adding his earnings from delivering newspapers ($37) gives the total amount he makes in one week, which is $79.50.
Joan is buying airline tickets for her family. Each airline ticket costs $232 with a baggage fee of $13. The airline charges a booking fee of $45 for the entire set of tickets. Joan spent a total of $1,515. If x represents the number of tickets, which equation can be used to find the value of x?
245 + 45 x = 1,515
232 x + 45 x = 1,515
232 x + 45 = 1,515
245 x + 45 = 1,515
The equation that can be used to find the value of x is:
232x + 13x + 45 = 1515
This is because each ticket costs $232 plus a baggage fee of $13, and Joan is buying x tickets. The airline also charges a booking fee of $45 for the entire set of tickets. Adding the total cost of the tickets and the booking fee gives the total amount Joan spent on the tickets, which is $1515.
Simplifying the equation:
245x + 45 = 1515
Thus, the equation that can be used to find the value of x is 245x + 45 = 1515.
A theater holds 2,680 seats. The lower level has 100 less than 2 times as many seats as the upper level. The middle level has 80 more than 3 times as many seats as the upper level. How many seats are in the middle level?
450 seats
800 seats
1,250 seats
1,430 seats
Let's say the number of seats in the upper level is "x". Then we can translate the given information into equations:
- The total number of seats is 2680:
x + (2x - 100) + (3x + 80) = 2680
- Simplifying this equation:
6x - 20 = 2680
- Solving for "x":
6x = 2700
x = 450
So, the upper level has 450 seats, the lower level has 2x-100 = 800 seats, and the middle level has 3x+80 = 1430 seats.
Therefore, the middle level has 1,430 seats.
The perimeters of the square and the regular pentagon are equal.
A square with side lengths of 3x + 3. A pentagon with side lengths of x + 8.
What is the perimeter of each polygon?
12
15
42
60
The perimeter of a square is given by the formula:
Perimeter = 4s,
where s is the length of a side.
So, the perimeter of the given square with side lengths of 3x+3 is:
Perimeter = 4(3x+3) = 12x + 12
The perimeter of a regular pentagon is given by the formula:
Perimeter = 5s,
where s is the length of a side.
So, the perimeter of the given pentagon with side lengths of x+8 is:
Perimeter = 5(x+8) = 5x + 40
Since the perimeters of the square and the pentagon are equal, we can set the two expressions equal to each other and solve for x:
12x + 12 = 5x + 40
7x = 28
x = 4
Now we can substitute x=4 into the expressions for the perimeters:
Perimeter of square = 12x + 12 = 12(4) + 12 = 60
Perimeter of pentagon = 5x + 40 = 5(4) + 40 = 60
Therefore, the perimeter of each polygon is 60.
A football stadium holds 17,700 seats. The lower level has 300 seats less than 4 times the number of seats in the upper level. The middle level has 500 more seats than twice the number of seats in the upper level. Let x represent the seats in the upper level. Which equation can be used to find the number of seats in the upper level?
7 x + 200 = 17,700
6 x + 200 = 17,700
7 x minus 200 = 17,700
6 x minus 200 = 17,700
The given information can be translated into equations as:
- The total number of seats is 17,700:
Upper level seats + Lower level seats + Middle level seats = 17,700
- The lower level has 300 seats less than 4 times the number of seats in the upper level:
Lower level seats = 4x - 300
- The middle level has 500 more seats than twice the number of seats in the upper level:
Middle level seats = 2x + 500
Substituting the expressions for lower and middle level seats into the first equation gives:
Upper level seats + (4x - 300) + (2x + 500) = 17,700
Simplifying:
7x + 200 = 17,700
So, the equation that can be used to find the number of seats in the upper level is:
7x + 200 = 17,700.
Kendall scored 3 times as many points as Abdul scored in a basketball game. Otis scored 5 more points than Abdul scored. The three players scored 45 points all together. How many points did each player score?
Kendall: 24 points; Abdul: 13 points; Otis: 8 points
Kendall: 8 points; Abdul: 8 points; Otis: 8 points
Kendall: 24 points; Abdul: 8 points; Otis: 13 points
Kendall: 8 points; Abdul: 13 points; Otis: 24 points
Let's say that Abdul's score is "x". Then, Kendall's score would be 3 times as many points, or 3x, and Otis's score would be 5 more points than Abdul's score, or x+5.
We're told that the three players scored 45 points all together, so we can write an equation:
x + 3x + (x+5) = 45
Simplifying and solving for "x":
5x + 5 = 45
5x = 40
x = 8
So Abdul scored 8 points, Kendall scored 3 times as many points, or 24 points, and Otis scored 5 more points than Abdul, or 13 points.
Therefore, Abdul scored 8 points, Kendall scored 24 points, and Otis scored 13 points.