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.
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A. The two quantities we need to find are the number of pounds of strawberry candy (s) and the number of pounds of chocolate candy (c) that should be used to make the desired mixture.
B. To find the total number of pounds in the mixture, we can use the given information that the mixture should be 17 pounds. So we can write the equation: s + c = 17.
C. To find the total cost of the mixture, we can use the given information that the mixture should be worth $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. So we can write the equation: 2.48s + 3.50c = 50.32.
D. The two equations from parts B and C can be written as a system of linear equations:
s + c = 17
2.48s + 3.50c = 50.32
We can solve this system of equations using the substitution method or the addition method.
E. In this problem, the variable s represents the number of pounds of strawberry candy, and the variable c represents the number of pounds of chocolate candy. The solution to the system of equations will give us the specific values for s and c that should be used to make the desired mixture.