Jane's sweet shop mixes candy worth 80 cents per pound with candy worth 2 dollars per pound to make 20 pounds of a mixture worth 1.60 per pound. How many pounds of each kind of candy does the store use?
80 a +200 b = 160 *20 = 3200
and
a + b = 20 so b=20-a
80 a + 200(20-a) = 3200
80 a + 4000 -200 a = 3200
120 a = 800
12 a = 80
a = 6 2/3 pounds
so b = 20-a = 13 1/3 pounds
To solve this problem, we can set up a system of equations based on the given information. Let's represent the unknowns as follows:
Let x be the number of pounds of candy worth 80 cents per pound.
Let y be the number of pounds of candy worth 2 dollars per pound.
We can then set up the following equations:
Equation 1: x + y = 20 (since there are 20 pounds of the mixture)
Equation 2: (0.80x + 2.00y) / 20 = 1.60 (since the average price of the mixture is 1.60 per pound)
To solve this system of equations, we can use the substitution method. Let's solve Equation 1 for x:
x = 20 - y
Next, substitute this value of x into Equation 2:
(0.80(20-y) + 2.00y) / 20 = 1.60
Simplifying this equation, we get:
16 - 0.80y + 2.00y = 1.60 * 20
16 + 1.20y = 32
1.20y = 16
y = 16 / 1.20
y = 13.33
However, we need to have a whole number of pounds, so we can't have 13.33 pounds of the candy worth 2 dollars per pound. We should round down to the nearest whole number, which gives us:
y = 13 pounds
Now, substitute this value of y back into Equation 1 to solve for x:
x + 13 = 20
x = 20 - 13
x = 7
Therefore, Jane's sweet shop uses 7 pounds of candy worth 80 cents per pound and 13 pounds of candy worth 2 dollars per pound to make the 20 pounds of mixture worth 1.60 per pound.