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.
A. The two quantities we are asked to find are the amount of strawberry candy and the amount of chocolate candy that should be used to make the desired mixture. Let's label the amount of strawberry candy as "s" and the amount 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" gives us information about the cost per pound of each candy and the desired cost per pound of the mixture. To find the total cost of the mixture, we can multiply the cost per pound of the mixture ($2.96) by the total weight of the mixture (17 pounds). So we can write the equation: 2.48s + 3.50c = 2.96 * 17.
D. The two equations from parts (B) and (C) are:
Equation 1: s + c = 17
Equation 2: 2.48s + 3.50c = 2.96 * 17
Now we can solve this system of linear equations using either the substitution method or the addition method.
E. In this word problem, the variable "s" represents the amount of strawberry candy in pounds, and the variable "c" represents the amount of chocolate candy in pounds. The sentence that answers the question posed in the problem is: The candy store needs to use s pounds of strawberry candy and c pounds of chocolate candy to form a 17-pound mixture.