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?
Step by step please
Step 1: Define the variables:
Let l represent the number of CDs Ms. Kitts sold last week.
Let t represent the number of CDs Ms. Kitts sold this week.
Step 2: Write the system of equations:
From the given information, we know that Ms. Kitts sold a total of 110 CDs over the two weeks. We can use this information to create an equation:
l + t = 110 (equation 1)
The problem also states that last week she sold 6 more than 3 times the number of CDs she sold this week. This can be written as an equation:
l = 3t + 6 (equation 2)
Step 3: Solve for all variables:
Now we have a system of equations with two variables, l and t.
We can solve this system of equations using substitution or elimination method.
Substitution Method:
We solve equation 2 for l and substitute it into equation 1:
l = 3t + 6 (equation 2)
Substituting l in equation 1: (3t + 6) + t = 110
Simplifying: 4t + 6 = 110
Subtracting 6 from both sides: 4t = 104
Dividing both sides by 4: t = 26
Now substitute the value of t back into equation 1 to find the value of l:
l + t = 110
l + 26 = 110
Subtracting 26 from both sides: l = 84
So, the solution to the system of equations is l = 84 and t = 26.
Therefore, Ms. Kitts sold 84 CDs last week and 26 CDs this week.
To solve this word problem, we first need to define variables. Let's represent the number of CDs Ms. Kitts sold last week as "l" and the number of CDs she sold this week as "t."
According to the problem, Ms. Kitts sold 6 more than 3 times the number of CDs this week. This can be expressed as:
l = 3t + 6 ------ Equation (1)
The problem also states that Ms. Kitts sold a total of 110 CDs over the two weeks. So, the sum of the CDs sold last week (l) and the CDs sold this week (t) is equal to 110:
l + t = 110 ------ Equation (2)
We now have a system of equations:
Equation (1): l = 3t + 6
Equation (2): l + t = 110
To solve for the variables "l" and "t," we can use the method of substitution or elimination. Let's use the method of substitution.
From Equation (1), we can solve for "l":
l = 3t + 6
Next, substitute this value of "l" into Equation (2):
(3t + 6) + t = 110
Combine like terms:
4t + 6 = 110
Subtract 6 from both sides:
4t = 104
Divide both sides by 4:
t = 26
Now that we have the value of "t" (number of CDs sold this week), we can substitute it back into Equation (1) to find the value of "l" (number of CDs sold last week):
l = 3t + 6
l = 3(26) + 6
l = 78 + 6
l = 84
Therefore, Ms. Kitts sold 84 CDs last week and 26 CDs this week.
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.