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Answer:
20 pounds
Step-by-step explanation:
Let x represent the number of pounds of lollipops and y represent the number of pounds of caramel candies. The first equation is
x + y = 30,
since the combined numbers of pounds of lollipops and caramel candies.
The lollipops sell for 0.95/lb; this gives us the expression 0.95x.
Caramel candies sell for 1.10/lb; this gives us the expression 1.10y.
Together they make a 30 pound mixture that sells for 1.00/lb; this gives us the expression 30(1.00), which simplifies to 30.
This together gives us the equation
0.95x+1.10y = 30
This gives us the system
[tex]\left \{ {{x+y=30} \atop {0.95x+1.10y=30}} \right.[/tex]
To solve this we will use elimination; we will make the coefficients of x the same by multiplying the top equation by 0.95:
[tex]\left \{ {{0.95(x+y=30)} \atop {0.95x+1.10y=30}} \right. \\\\\left \{ {{0.95x+0.95y=28.5} \atop {0.95x+1.10y=30}} \right.[/tex]
Subtract the second equation from the first:
[tex]\left \{ {{0.95x+0.95y=28.5} \atop {-(0.95x+1.10y=30)}} \right. \\\\-0.15y=-1.5[/tex]
Divide both sides by -0.15:
-0.15y/-0.15 = -1.5/-0.15
y = 10
There are 10 pounds of caramel candies.
Substitute this into the first equation:
x+10 = 30
Subtract 10 from each side:
x+10-10 = 30-10
x = 20
There are 20 pounds of lollipops.
The pounds of lollipop in the mixture is 20 pounds.
Two equations can be derived from the question:
a + b = 30 equation 1
0.95a + 1.10b = 30 equation 2
a = pounds of lollipop in the mixture
b = pounds of caramel in the mixture.
This set of equations are known as simultaneous equations. They would be solved using the elimination method.
The first step is to multiply equation 1 by 1.1
1.1a + 1.1b = 33 equation 3
The second step is to subtract equation 2 from 3
0.15a = 3
To determine the vale of a, divide both sides of the equation by 0.15
a = 3 / 0.15
a = 20 pounds
To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults
