I'm still having trouble with this
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?
To approach word problems, you could follow the steps:
1. Read and understand the problem, identify the unknown to be calculated.
2. Designate an algebraic symbol to stand for the unknown, or one of the unknowns.
3. Reread the question, interpret the information given in terms of the unknowns.
In the case where a simple relationship relates two or more unknowns, express the other unknowns in terms of the one that has an algebraic symbol.
4. Formulate a mathematical equation in terms of the algebraic symbol.
5. Solve for the unknown, if possible. Evaluate the other unknowns expressed in terms of the algebraic symbol.
6. Interpret the results in words.
7. Check the calculated results.
The example given will illustrate the procedure.
1. Unknowns to be calculated: quantities sold by DQ and Sonic.
2. Since a simple relationship relates the two ("DQ sells 6 times as many orders of french fries as sonic everyday."), we will designate only one variable,
S = initial daily sales by Sonic
3. Reread the question:
"DQ sells 6 times as many orders of french fries as sonic everyday."
6S = daily sales by DQ
"If both sold 60 more orders DQ would only sell 3 times as many fries."
Noting that we denote initial sales of DQ by 6S:
3 times (S+60 more sales) = (6S + 60 more sales)
4. Formulate an equation
From (3) above, we conclude that the equation is:
3(S + 60) = (6S + 60)
5. Solve the equation:
Expand the terms:
3S + 3*60 = 6S + 60
3S + 180 = 6S + 60
Collect terms containing S on the left-hand side:
3S - 6S = 60 - 180
-3S = -120
Solve for S:
S = -120 / (-3) = 40
6. Interpret the results:
S=40= initial sales by Sonic.
6S = 240 = initial sales by DQ
S+60 = 100 = increase sales by sonic
6S+60 = 300 = increased sales by DQ
7. Check:
240/40 = 6 times (OK)
(240+60)/(40+60) = 300/100 = 3 times (OK)
Petie--I gave you two equations yesterday and told you to solve the two simultaneous equations. Matmate gave you some very good directions as a way to approach word problems. Perhaps you need to review the mechanics of how to solve simultaneous equations, also.
To solve this problem, let's break it down step by step:
Step 1: Assign variables
Let's use the variables "DQ" and "Sonic" to represent the number of orders they sell before the increase. We will also use "DQ_new" and "Sonic_new" to represent the number of orders they would sell after the increase.
Step 2: Set up equations based on the problem
The problem states that DQ sells 6 times as many orders of french fries as Sonic every day. Mathematically, we can write this as:
DQ = 6 * Sonic
The problem also states that if both DQ and Sonic sold 60 more orders, DQ would only sell 3 times as many fries as Sonic. We can write this as:
DQ_new = 3 * (Sonic_new + 60)
Step 3: Solve the equations
Now we have two equations with two variables. We can substitute the value of DQ from the first equation into the second equation to solve for Sonic.
Substituting the value of DQ from the first equation into the second equation:
6 * Sonic_new = 3 * (Sonic_new + 60)
Simplifying the equation:
6 * Sonic_new = 3 * Sonic_new + 180
3 * Sonic_new = 180
Sonic_new = 180 / 3
Sonic_new = 60
Step 4: Calculate the other variables
Now that we have found the value for Sonic_new, we can substitute it back into the first equation to find the value for DQ_new:
DQ_new = 6 * Sonic_new
DQ_new = 6 * 60
DQ_new = 360
Since the problem asks for the number of orders they sell before and after the increase, we can substitute the value of Sonic_new into the first equation to find the values for Sonic and DQ:
DQ = 6 * Sonic
DQ = 6 * 60
DQ = 360
So, before the increase, DQ sells 360 orders of fries and Sonic sells 60 orders of fries. After the increase, DQ sells 360 orders of fries and Sonic sells 60 orders of fries.