SOLUTION: In a certain store, blue shirts are one-fifth the price of red shirts. If b blue shirts cost d dollars, what is the cost of r red shirts?
a) 5dr
b) 5brd
c) (rd)/(5b)
d) (5rd)/b
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Question 1190484: In a certain store, blue shirts are one-fifth the price of red shirts. If b blue shirts cost d dollars, what is the cost of r red shirts?
a) 5dr
b) 5brd
c) (rd)/(5b)
d) (5rd)/b
e) (5br)/d
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x the cost of 1 blue shirt.
let y = the cost of 1 red shirt.
the price of b blue shirts is therefore equal to b * x.
the price of r red shirts is therefore equal to r * y.
you are given that the price of 1 blue shirt is equal to 1/5 * the price of 1 red shirt.
the equation for that is x = 1/5 * y
multiply both sides of that equation by 5 to get:
y = 5 * x
this says that the price of 1 red red shirt is equal to 5 * the price of 1 blue shirt.
the price of r red shirts is therefore equal to r * 5 * x
since the price of b blue shirts is equal to b * x which is equal to d, you get:
b * x = d
solve for x to get:
x = d/b
the price of r red shirts, which is r * 5 * x, becomes r * 5 * d/b
this is the same as 5rd/b which is selection d.
that should be your answer.
i did an analysis to see if this is correct.
my analysis is shown below:
let the cost of a blue shirt = 10
let the cost of a red shirt = 5 * 10 = 50
let the number of blue shirts = 8
let the number of red shirts = 20
the cost of 8 blue shirts is 8 * 10 = 80
the cost of 20 red shirts if 20 * 50 = 1000
the formula states that the cost of r red shirts = 5rd/b
since r = 20 and d = 80 and b = 8, you get:
the cost of r red shirts = 5 * 20 * 80 / 8 which is equal to 1000.
this confirms the formula is correct.
answer is selection d which is equal to 5rd/b.
let me know if you have any quesions.
theo
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