Let l be the number of CDs she sold last week, and t be the number of CDs she sold this week.
According to the problem, Ms. Kitts sold 6 more than 3 times the number of CDs that she sold this week last week. This can be expressed in the equation: l = 3t + 6.
We also know that the total number of CDs sold over the 2 weeks is 110. This can be expressed in the equation: l + t = 110.
Therefore, the system of equations to solve for l and t is:
l = 3t + 6
l + t = 110
To solve this system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
From the first equation, we can express l in terms of t:
l = 3t + 6
Substitute this expression for l in the second equation:
(3t + 6) + t = 110
Simplify the equation:
4t + 6 = 110
Subtract 6 from both sides:
4t = 104
Divide both sides by 4:
t = 26
Substitute this value of t back into the first equation 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.
Method 2: Elimination
Rearrange the second equation to isolate l:
l = 110 - t
Substitute this expression for l in the first equation:
110 - t = 3t + 6
Combine like terms:
110 - 6 = 3t + t
104 = 4t
Divide both sides by 4:
t = 26
Substitute this value of t back into the second equation to find l:
l + 26 = 110
l = 110 - 26
l = 84
Therefore, Ms. Kitts sold 84 CDs last week and 26 CDs this week.
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?
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