A yoga studio has two participation plans. For the first plan, the cost is $8 per visit. For the second plan, the cost is $40 per month, and $2 per visit. Write an equation to show the number of visits per month that it would take for the two plans to be equal. Use x as your variable. Write *ONLY* the equation.
8x = 40 + 2x
Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. When will the two vats have the same amount of liquid?
Let t be the number of minutes it takes for the two vats to have the same amount of liquid.
The amount of liquid in the first vat after t minutes is given by 6t, and the amount of liquid in the second vat after t minutes is given by 28 + 4t.
Since the two vats will have the same amount of liquid when t minutes have passed, we can set the two expressions equal to each other:
6t = 28 + 4t
Solving for t:
6t - 4t = 28
2t = 28
t = 14
Therefore, it will take 14 minutes for the two vats to have the same amount of liquid.
Movie Theatre A has a popcorn machine with a 100-gallon capacity, and sells 3 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity, and sells 5 gallons of popcorn per hour. Write an equation to show when the two popcorn machines will have the same amount of popcorn left. Use x as your variable.
1.) 100 + 3x = 150 + 5x
2.) 3x − 100 = 5x − 150
3.) 150 + 3x = 100 + 5x
4.) 100 − 3x = 150 − 5x
1.) 100 + 3x = 150 + 5x
Two machines at a factory are filling cans of soup. One machine has filled 92 cans of soup. It fills cans at a rate of 16 cans per minute. The second machine has filled 104 cans of soup. It fills cans at a rate of 13 cans per minute. Write and solve an equation to show when the two machines will have filled the same number of cans of soup.
1.) 104 + 16x = 92 + 13x ; x = 4
2.) 92 − 16x = 104 − 13x ; x = −4
3.) 92 + 16x = 104 + 13x ; x = 6
4.) 92 + 16x = 104 + 13x ; x = 4