DQ sells 6 times as many orders of french fries as sonic everyday. If both sold 60 more orders DQ would only sell 3 times as many fries. How many do each sell before and after the incease?
S = number FF Sonic sells.
D = number FF DQ sells.
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D = 6S every day.
If each sells 60 more, then
D + 60 = 3(S + 60) or
D + 60 = 3S + 120 or
D = 3S + 120
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The two equators are as follows:
D = 6S
D = 3S + 120
Solve these two simultaneous equation for D and S (before the addition of 60), then add 60 to each to determine the number sold after adding 60 to each. Post your work if you get stuck.
Where did the 120 come from?
To solve this problem, let's first assign variables to the quantities mentioned in the question. Since we are looking for the number of orders of french fries sold by each restaurant, we can represent DQ's sales as "DQ" and Sonic's sales as "Sonic".
According to the information given:
1. DQ sells 6 times as many orders of french fries as Sonic everyday. Mathematically, we can write this as:
DQ = 6 * Sonic
2. If both DQ and Sonic sold 60 more orders, DQ would only sell 3 times as many fries. Mathematically, we can write this as:
(DQ + 60) = 3 * (Sonic + 60)
Now we can solve these two equations to find the number of fries sold by each restaurant.
First, substitute the value of DQ from the first equation into the second equation:
6 * Sonic + 60 = 3 * (Sonic + 60)
Expand the equation:
6 * Sonic + 60 = 3 * Sonic + 180
Simplify the equation:
6 * Sonic - 3 * Sonic = 180 - 60
3 * Sonic = 120
Divide both sides of the equation by 3:
Sonic = 120 / 3
Sonic = 40
Now substitute the value of Sonic back into the first equation to find the value of DQ:
DQ = 6 * Sonic
DQ = 6 * 40
DQ = 240
Therefore, before the increase in orders, Sonic sells 40 orders of french fries and DQ sells 240 orders of french fries.
After the increase, Sonic sold 40 + 60 = 100 orders of french fries, and DQ sold 240 + 60 = 300 orders of french fries.