2. Solving systems of equations word problems worksheet For all problems, define variables, write the system of equations and solve for all variables.
-Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 110 CDs over the 2 weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week?
Let l be the number of CDs Ms. Kitts sold last week, and t be the number of CDs she sold this week.
From the given information, we can write the following equations:
1) l = 3t + 6 (Ms. Kitts sold 6 more than 3 times the number of CDs she sold this week)
2) l + t = 110 (Ms. Kitts sold a total of 110 CDs over the 2 weeks)
Therefore, the system of equations that can be used to find l and t is:
l = 3t + 6
l + t = 110
To solve this word problem, we need to define two variables:
l = the number of CDs Ms. Kitts sold last week
t = the number of CDs Ms. Kitts sold this week
According to the problem, Ms. Kitts sold 6 more than 3 times the number of CDs she sold this week last week. So, the equation representing this relationship is:
l = 3t + 6 (Equation 1)
The problem also states that Ms. Kitts sold a total of 110 CDs over the two weeks. Therefore, we can set up the equation:
l + t = 110 (Equation 2)
Now we have a system of equations:
l = 3t + 6
l + t = 110
To solve this system, you can use substitution or elimination method. Let's use the substitution method:
Take Equation 1: l = 3t + 6
Replace l in Equation 2 with its value from Equation 1:
(3t + 6) + t = 110
Simplify the equation:
4t + 6 = 110
Subtract 6 from both sides:
4t = 104
Divide both sides by 4:
t = 26
Now substitute this value of t back into Equation 1 to find l:
l = 3(26) + 6
l = 78 + 6
l = 84
Therefore, Ms. Kitts sold 84 CDs last week and 26 CDs this week.
To solve this problem, let's define the variables:
l = the number of CDs Ms. Kitts sold last week
t = the number of CDs Ms. Kitts sold this week
The problem states that Ms. Kitts sold a total of 110 CDs over the 2 weeks, so we can write the first equation:
l + t = 110
The problem also states that last week she sold 6 more than 3 times the number of CDs she sold this week. We can translate this into the second equation:
l = 3t + 6
So, the system of equations to solve for the variables l and t is:
l + t = 110
l = 3t + 6
Now we can solve it. We will use the substitution method:
1. Rewrite the first equation as l = 110 - t.
2. Substitute this expression for l in the second equation: 110 - t = 3t + 6.
3. Simplify the equation: 110 - 6 = 3t + t.
-> 104 = 4t
4. Divide both sides of the equation by 4 to isolate t: t = 104/4.
5. Simplify: t = 26.
6. Now substitute the value of t into the first equation to solve for l: l + 26 = 110.
7. Subtract 26 from both sides of the equation: l = 110 - 26.
8. Simplify: l = 84.
Therefore, Ms. Kitts sold 84 CDs last week and 26 CDs this week.