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Javier and Brianna both have summer jobs working at Honeybee Ice Cream. Javier makes $15 per hour, and he has already earned a total of $270 this summer. Brianna is starting today, and she will be making $18 per hour as a new manager. Javier and Brianna work the same schedule.
Which equation can you use to find h, the number of hours of work it will take for Brianna and Javier to have earned the same amount of money?
How many hours of work will it take for Brianna and Javier to have earned the same amount of money?
The equation that can be used to find h, the number of hours of work it will take for Brianna and Javier to have earned the same amount of money is:
15h + 270 = 18h
Now, we can solve for h:
270 = 3h
h = 90
Therefore, it will take 90 hours of work for Brianna and Javier to have earned the same amount of money.
The equation that can be used to find s, the number of shirts Meg would need to order for the two options to cost the same is:
11s + 100 = 15s + 24
Now, we can solve for s:
100 - 24 = 15s - 11s
76 = 4s
s = 19
Therefore, Meg would need to order 19 shirts for the two options to cost the same.
To find the number of months it would take for the total cost at either gym to be the same, we can set up the following equation:
45m + 20 = 37.50m + 65
Where:
45m represents the total cost at Infinity Fitness
37.50m represents the total cost at Power Zone
Now, we'll solve for m:
45m + 20 = 37.50m + 65
45m - 37.50m = 65 - 20
7.50m = 45
m = 45 / 7.50
m = 6
Therefore, it would take 6 months for the total cost at either gym to be the same.
As president of the student council, Meg is choosing between two options for class T-shirts. A local shop charges $11 for each shirt, plus a set-up fee of $100. An online store charges $15 for each shirt, plus a set-up fee of $24.
Which equation can you use to find s, the number of shirts Meg would need to order for the two options to cost the same?
How many shirts would Meg need to order for the two options to cost the same?
Last Saturday, Erin and Krysta each biked the Prairie Point Trail, a 20-mile path leading to the peak of Prairie Point Mountain. Both girls started at 7:00 A.M., heading toward the peak. Erin started at the trailhead and biked at a constant speed of 10 miles per hour. Krysta started at an entry point 3 miles ahead of the trailhead and rode at a steady pace of 8 miles per hour.
If each girl kept a constant speed, which equation can you use to find h, the number of hours it took for Erin to catch up to Krysta?
How long did it take for Erin to catch up to Krysta?
Simplify any fractions.
To find the time it took for Erin to catch up to Krysta, we can set up the following equation based on the distances they covered:
Distance = Rate x Time
Let h be the number of hours it took for Erin to catch up to Krysta. Since Erin biked 10 miles per hour and Krysta biked 8 miles per hour, the distances covered by each girl in h hours would be:
Distance covered by Erin = 10h
Distance covered by Krysta = 8h + 3
According to the given information, both girls covered the same total distance, which is the length of the trail, 20 miles. Setting the two distances equal to each other gives us the equation:
10h = 8h + 3 + 20
Now, solve for h:
10h = 8h + 23
10h - 8h = 23
2h = 23
h = 23 / 2
h = 11.5
It took Erin 11.5 hours to catch up to Krysta on the Prairie Point Trail.
Nick wants to join a gym, and he is deciding between two options. Infinity Fitness charges $45 per month, plus a one-time registration fee of $20. The Power Zone charges $37.50 per month, plus a one-time registration fee of $65.
Which equation can you use to find m, the number of months it would take for the total cost at either gym to be the same?
After how many months would the total cost at either gym be the same?
Coach Liz and Coach Joseph were stocking up on snacks for their soccer teams. Liz bought some juice boxes along with some oranges that cost $10.98. Joseph bought three times as many juice boxes as Liz, but he didn't buy any oranges. He spent the same amount of money as Liz.
Which equation can you use to find b, the amount of money Liz spent on juice boxes?
How much did Liz spend on juice boxes?
Let's denote:
- the cost of one juice box as j
- the number of juice boxes Liz bought as n
- the total amount Liz spent on juice boxes as b
From the given information:
- Liz bought some juice boxes along with some oranges that cost $10.98
- Joseph bought three times as many juice boxes as Liz but spent the same amount of money as Liz
The equation we can use to find b (the amount Liz spent on juice boxes) is:
n*j = b
Joseph bought three times as many juice boxes as Liz, which means Joseph bought 3n juice boxes. If Joseph spent the same amount of money as Liz and didn't buy any oranges, then we can set up another equation:
3n*j = 10.98
Since Liz only bought juice boxes and oranges that cost $10.98, we can write:
n*j + 10.98 = b
Combining the equations:
n*j + 10.98 = 3n*j
Now, we can solve for b:
10.98 = 2n*j
b = 2n*j
Therefore, the amount of money Liz spent on juice boxes is $10.98.