Question 472652: I need help with getting the alegbra equations from this word problem. Please help.
1.Marco attended a concert at which two bands were playing. The opening act, The Fray, performed for m minutes. The second band, 3 doors down, performed for 30 minutes longer than the Fray. the total time the bands performed was 200 minutes. Write an equation represting the length of the entire concert.
2. The width of a retangle is 10 inches shorter than its length. If the lenght is l, write the equation you would use to find the area of the retangle if the area is 56 square inches.
3.Because water cools very slowly, the temperature at the bottom of large of water goes down to, never below, 39.2F. If the temperature is T, write an inequality showing the temperature at the bottom of Lake erie right now.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! problem 1:
fray performed for m minutes.
3 doors down performed for 30 minutes longer than fray.
total time both bands performed was 200 minutes.
equations representing the length of the entire concert would be:
m = number of minutes fray performed.
m + 30 = number of minutes 3 doors down performed.
m + m + 30 = 200
2m + 30 = 200
2m = 170
m = 85 minutes
m + 30 = 115 minutes
total time = 85 + 115 = 200 minutes
equation representing length of the entire concert is:
2m + 30 = 200
problem 2:
if the width of a rectangle is 10 inches shorter than the length and the length is 1, then the width of the rectangle would have to be -9.
this is not possible so there's something wrong with your problem statement.
if the area of the rectangle is 56 square inches, then:
width * lengthy = 56 square inches.
if the width is 10 inches less than the length, and we let the length be equal to x, then the width is equal to x-10 and the formula becomes:
x * (x-10) = 56
this formula becomes:
x^2 - 10x = 56
subtract 56 from both sides of this equation to get:
x^2 - 10x - 56 = 0
this looks like it can be factored as follows:
(x-14) * (x + 4) = 0
this makes x = 14 or x = -4.
x can't be negative, so x has to be 14.
this makes x - 10 = 4
the length is 14 and the width is 4.
4 * 14 = W * L = 56 square inches.
we're good.
problem 3:
T >= 39.2
this means that the temperature is equal to or greater than 39.2 degrees fahrenheit.
the temperature at the bottom of lake Erie is equal to T and T is greater than or equal to 39.2 degrees Fahrenheit.
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