5.) Simone owns a candy store and wishes to mix strawberry candy worth $2.48 per pound with chocolate candy worth $3.50 per pound to form 17 pounds of a mixture worth $2.96 per pound. Write and solve a system of linear equations to find how many pounds of each type of candy should be used to make the desired mixture.
A.What are the two quantities you are asked to find? Be specific. Label one of the quantities, and the other(or choose your own variables).
B.Focusonthephrase,“...form 17 pounds of a mixture...”.Think about the meaning of andy from part (a) and then write an equation containing the variables and the “total” number.
C.) Focus on the phrase,“...mix strawberry candy worth $2.48 per pound with chocolate candy worth $3.50 per pound to form 17 pounds of a mixture worth $2.96 per pound”. Thinkaboutthemeaningofxandyfrompart(a)and then write an equation containing the variables and the “total” number. Hint: The “total” number needs to be calculated. If youweretobuy17poundsof candyat$2.96perpound, what is the total you would pay? Each term this equation will follow the same pattern.
D.) Re-write the two equations from parts (b)and(c).Thisisasystemoflinearequations.Solve the system by using either the substitution method or the addition method
4c.Focusonthephrase,“...mixstrawberrycandyworth$2.48perpoundwithchocolatecandyworth $3.50 per pound to form 17 pounds of a mixture worth $2.96 per pound”.
E.) For an application (word problem) do not express the solution as a set. Refer to part (a).Whatdoeseachvariablemean?Write a brief sentence answering the question posed in the problem. Be sure to attach the appropriate unit to each number value.
The solution to the system of linear equations is x = 8 pounds of strawberry candy and y = 9 pounds of chocolate candy. This means that Simone should use 8 pounds of strawberry candy worth $2.48 per pound and 9 pounds of chocolate candy worth $3.50 per pound to form 17 pounds of a mixture worth $2.96 per pound.
A. The two quantities we are asked to find are the pounds of strawberry candy (let's call it x) and the pounds of chocolate candy (let's call it y) that should be used to make the desired mixture.
B. The phrase "form 17 pounds of a mixture" tells us that the total weight of the candy mixture should be 17 pounds. This can be expressed as the equation:
x + y = 17
C. The phrase "mix strawberry candy worth $2.48 per pound with chocolate candy worth $3.50 per pound to form 17 pounds of a mixture worth $2.96 per pound" tells us that the total cost of the candy mixture is $2.96 per pound. If we were to buy 17 pounds of candy at $2.96 per pound, the total cost would be:
17 * 2.96 = 50.32
Using this information, we can calculate the total cost of the strawberry candy and the chocolate candy using the given prices. The equation for the total cost is:
2.48x + 3.50y = 50.32
D. Re-writing the two equations from parts (b) and (c) gives us the system of linear equations:
x + y = 17
2.48x + 3.50y = 50.32
We can solve this system of equations using the substitution method or the addition method to find the values of x and y.
E. Variable x represents the pounds of strawberry candy, and variable y represents the pounds of chocolate candy needed to make a candy mixture. The solution to this problem will give us the specific quantities for x and y, which represent the pounds of each type of candy that should be used to create the desired mixture. The unit for weight could be pounds (lb) or kilograms (kg), depending on the given units.
A. The two quantities we are asked to find are the number of pounds of strawberry candy and the number of pounds of chocolate candy needed to make the desired mixture. We can label the number of pounds of strawberry candy as 's' and the number of pounds of chocolate candy as 'c'.
B. The phrase "form 17 pounds of a mixture" means that the total weight of the mixture should be 17 pounds. So we can write the equation: s + c = 17.
C. The phrase "mix strawberry candy worth $2.48 per pound with chocolate candy worth $3.50 per pound to form 17 pounds of a mixture worth $2.96 per pound" means that the average price per pound of the candy mixture should be $2.96. To calculate the average price, we need to find the total cost of strawberry candy and the total cost of chocolate candy, then divide it by the total weight of the mixture.
The total cost of strawberry candy is 2.48s dollars and the total cost of chocolate candy is 3.50c dollars. If we mix them to form 17 pounds of candy at $2.96 per pound, the total cost would be 2.96 * 17 = 50.32 dollars.
So we can write the equation: 2.48s + 3.50c = 50.32.
D. The two equations from parts (b) and (c) are:
1. s + c = 17
2. 2.48s + 3.50c = 50.32
To solve this system of equations, we can use the substitution method or the addition method. Let's use the addition method.
Multiply Equation 1 by 2.48 to get rid of the decimal:
2.48s + 2.48c = 41.84
Now subtract Equation 2 from this new equation:
(2.48s + 2.48c) - (2.48s + 3.50c) = 41.84 - 50.32
Simplify the equation:
2.48s + 2.48c - 2.48s - 3.50c = -8.48
Combine like terms:
(2.48s - 2.48s) + (2.48c - 3.50c) = -8.48
Simplify further:
-1.02c = -8.48
Divide both sides by -1.02 to solve for c:
c = (-8.48) / (-1.02)
c ≈ 8.31
Now substitute the value of c into Equation 1 to solve for s:
s + 8.31 = 17
Subtract 8.31 from both sides:
s = 17 - 8.31
s ≈ 8.69
Therefore, approximately 8.69 pounds of strawberry candy and 8.31 pounds of chocolate candy should be used to make the desired mixture.
E. In this problem, 's' represents the number of pounds of strawberry candy, and 'c' represents the number of pounds of chocolate candy needed to make the mixture. The sentence answering the question could be: "Simone needs approximately 8.69 pounds of strawberry candy and 8.31 pounds of chocolate candy to make a 17-pound mixture with an average price of $2.96 per pound."