A restaurant manager bought 20 packages
of bagels. Some packages contained 6 bagels
each, and the rest contained 12 bagels each.
There were 168 bagels in all. How many
packages of 12 bagels did the manager buy?
A 6
B 8
C 9
D 12
D 12
To determine the number of packages of 12 bagels the manager bought, we can set up an equation.
Let's assume x represents the number of packages of 6 bagels and y represents the number of packages of 12 bagels.
From the given information, we can create two equations:
Equation 1: x + y = 20 (the total number of packages)
Equation 2: 6x + 12y = 168 (the total number of bagels)
To solve this system of equations, we can use the method of substitution.
First, let's solve Equation 1 for x:
x = 20 - y
Now substitute this value of x into Equation 2:
6(20 - y) + 12y = 168
Simplifying the equation:
120 - 6y + 12y = 168
6y = 168 - 120
6y = 48
y = 48/6
y = 8
Therefore, the manager bought 8 packages of 12 bagels.
So, the answer is B) 8.
Let's solve this step-by-step:
Let's assume the number of packages that contained 6 bagels each be x, and the number of packages that contained 12 bagels each be y.
According to the problem, the total number of packages is 20. So we have the equation:
x + y = 20 ---(1)
Also, the total number of bagels is 168. We can express this as:
6x + 12y = 168 ---(2)
Now, we can use either substitution or elimination method to solve these equations. Let's use substitution method.
From equation (1), we have: x = 20 - y
Substituting this value of x in equation (2), we get:
6(20 - y) + 12y = 168
120 - 6y + 12y = 168
6y = 168 - 120
6y = 48
y = 48/6
y = 8
So, the manager bought 8 packages of 12 bagels each. Therefore, the answer is B) 8.