Sarah Comar's Candy Store sold a total of 57 jelly beans, selling two kinds of jelly beans. The first kind was priced at $4.73 per pound, and the second was priced at $0.84 per pound. In all, $121.79 was taken in for the two types of jelly beans. How many pounds of each kind were sold? (Let x represent the number of pounds of the first kind and y represent the number of pounds of the second
kind.)
x + y = 57 (Equation 1: The total number of pounds sold is 57.)
4.73x + 0.84y = 121.79 (Equation 2: The total revenue from selling both types of jelly beans is $121.79.)
We can solve this system of equations using substitution or elimination method.
Let's solve using the substitution method:
From Equation 1: x = 57 - y
Substitute the value of x in Equation 2:
4.73(57 - y) + 0.84y = 121.79
269.61 - 4.73y + 0.84y = 121.79
Combine like terms:
-3.89y = -147.82
Divide both sides by -3.89:
y = 147.82 / 3.89
y ≈ 37.98 pounds
Substitute the value of y in Equation 1:
x + 37.98 = 57
x ≈ 19.02 pounds
Therefore, approximately 19.02 pounds of the first kind and 37.98 pounds of the second kind were sold.
Step 1: Let's assume that x represents the number of pounds of the first kind of jelly beans sold.
So, y will represent the number of pounds of the second kind of jelly beans sold.
Step 2: We know that the first kind of jelly beans is priced at $4.73 per pound and the second kind is priced at $0.84 per pound.
Step 3: The total amount taken in for the two types of jelly beans is $121.79.
So, we can write the equation:
4.73x + 0.84y = 121.79
Step 4: We also know that a total of 57 jelly beans were sold.
Since the weight of jelly beans is not given, we can assume that the number of jelly beans sold is directly proportional to the weight of jelly beans.
So, we can write another equation:
x + y = 57
Step 5: Now we have a system of equations:
4.73x + 0.84y = 121.79
x + y = 57
Step 6: We can solve this system of equations using any method, such as substitution or elimination.
Let's use the elimination method to solve this system:
Step 7: Multiply the second equation by -4.73 to eliminate x:
-4.73(x + y) = -4.73(57)
-4.73x - 4.73y = -269.61
Step 8: Add the two equations:
4.73x + 0.84y + (-4.73x - 4.73y) = 121.79 + (-269.61)
0x - 3.89y = -147.82
Step 9: Solve for y:
-3.89y = -147.82
y = -147.82 / -3.89
y = 38
Step 10: Substitute the value of y into the second equation to find x:
x + 38 = 57
x = 57 - 38
x = 19
Step 11: Therefore, 19 pounds of the first kind of jelly beans were sold, and 38 pounds of the second kind of jelly beans were sold.
To solve this problem, we'll use a system of equations. Let's set up the equations based on the information given in the problem.
First, let's define the variables:
x = number of pounds of the first kind of jelly beans
y = number of pounds of the second kind of jelly beans
Now, let's set up the equations:
Equation 1: Total number of pounds sold
x + y = 57
Equation 2: Total revenue from the sales
4.73x + 0.84y = 121.79
We have a system of two equations with two unknowns. To solve it, we can use different methods like substitution or elimination. Let's use the substitution method.
Rearrange Equation 1 to solve for x:
x = 57 - y
Substitute this expression for x in Equation 2:
4.73(57 - y) + 0.84y = 121.79
Now, we can solve for y by simplifying and solving the resulting equation:
269.61 - 4.73y + 0.84y = 121.79
269.61 - 3.89y = 121.79
-3.89y = 121.79 - 269.61
-3.89y = -147.82
y = -147.82 / -3.89
y ≈ 37.99
To find x, substitute the value of y back into Equation 1:
x + 37.99 = 57
x = 57 - 37.99
x ≈ 19.01
Therefore, approximately 19.01 pounds of the first kind and 37.99 pounds of the second kind of jelly beans were sold.