Question 1167781: A clothes store sells boots, shoes and shirts. Each day, on
average, three times as many shoes are sold as boots, and
eight times as many shirts as shoes. The price of shoes is
identical to that of boots - NIS 250, and the price of shirts is
half of that price. In the last month, the store was open 20
days, and its total income was NIS 480,000. How many shirts,
on average, were sold each day in the last month?
(NIS is Israeli Currency) I don't understand how to make this into an algebraic
equation. Please walk me through step by step.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number of boots sold each day.
since 3 times as many shoes as boots are sold each day, then ...
3 * x = the number of shoes sold each day.
since 3 times as many shirts as shoes are sold each day, then ...
8 * 3 * x = 24 * x shirts are sold each day.
to summarize, each day on average .....
x number of boots are sold.
3 * x number of shoes are sold.
24 * x number of shirts are sold.
since each pair of boots sells for 250 and each pair of shoes sells for 250 and each shirt sells for 125, then, for each day on average, .....
boot revenue = 250 * x
shoe revenue = 3 * 250 * x = 750 * x
shirt revenue = 24 * 125 * x = 3000 * x
multiply by 20, then, over a 20 day period, .....
boot revenue = 20 * 250 * x = 5000 * x
shoe revenue = 20 * 750 * x = 15000 * x
shirt revenue = 20 * 24 * 125 * x = 60,000 * x
total revenue over a 20 day period is equal to 80,000 * x
since total revenue over a 20 day period = 480,000, then solve for x to get:
x = 480,000 / 80,000 = 6
when x = 6, ....
x = 6 boots are sold each day on average.
3 * 6 = 18 shoes are sold each day on average.
24 * 6 = 144 shirts are sold each day on average.
144 shirts per day on average should be your solution, but that solution needs to be confirmed to make sure it's accurate.
over a 20 day period, .....
20 * 6 = 120 boots are sold.
20 * 18 = 360 shoes are sold.
20 * 144 = 2880 shirts are sold.
total revenue over the 20 day period is .....
120 * 250 + 360 * 250 + 144 * 125 = 480,000
value of 6 for x is confirmed to be good.
solution is that:
last month, 144 shirts were sold each day on average.
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