Question 472652
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.