SOLUTION: Set up equations and solve. You spent $125 on 90 snacks that include fruit and cookies. If fruit cost $2.50 each and cookies cost $1.25 each, how many of each did you buy?

Algebra ->  Matrices-and-determiminant -> SOLUTION: Set up equations and solve. You spent $125 on 90 snacks that include fruit and cookies. If fruit cost $2.50 each and cookies cost $1.25 each, how many of each did you buy?       Log On


   

Question 1193738: Set up equations and solve.
You spent $125 on 90 snacks that include fruit and cookies. If fruit cost $2.50 each and cookies cost $1.25 each, how many of each did you buy?

Found 3 solutions by ikleyn, Solver92311, MathTherapy:
Answer by ikleyn(52806) About Me  (Show Source):
You can put this solution on YOUR website!
.
Set up equations and solve.
You spent $125 on 90 snacks that include fruit and cookies.
If fruit cost $2.50 each and cookies cost $1.25 each, how many of each did you buy?
~~~~~~~~~~~~~~~~ 

Write equations as you read the problem

        F +     C =  90      (1)     (counting snacks)

    2.50F + 1.25C = 125      (2)     (counting money)


From equation (1), express  C = 90 - F   and substitute it into equation (2).  You will get

    2.50F + 1.25*(90-F) = 125.


Simplify and find F, the number of fruit snacks

    2.50F + 1.25*90 - 1.25F = 125

    2.50F - 1.25F = 125 - 1.25*90

        1.25F     =    12.5  

            F     =    12.5/1.25 = 10.


Thus you get the ANSWER:  there are 10 fruit snacks and 90-10 = 80 cookies snacks.


CHECK.  10*2.50 + 80*1.25 = 25 + 100 = 125 dollars,  total.   ! correct !

Solved.

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In this post, I showed you how the Substitution method works.

To learn more about solving systems of equations and associated word problem, see the lessons
    - Solution of the linear system of two equations in two unknowns by the Substitution method
    - Solution of the linear system of two equations in two unknowns by the Elimination method
    - Solution of the linear system of two equations in two unknowns using determinant
    - Geometric interpretation of the linear system of two equations in two unknowns
    - Solving word problems using linear systems of two equations in two unknowns

    - Word problems that lead to a simple system of two equations in two unknowns
    - Oranges and grapefruits
    - Using systems of equations to solve problems on tickets
    - Using systems of equations to solve problems on shares
    - Using systems of equations to solve problems on investment
    - Two mechanics work on a car
    - The Robinson family and the Sanders family each used their sprinklers last summer
    - Roses and violets
    - Counting calories and grams of fat in combined food
    - A theater group made appearances in two cities
    - Typical word problems on systems of 2 equations in 2 unknowns
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!










Solve for and then calculate


John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!
Set up equations and solve.
You spent $125 on 90 snacks that include fruit and cookies. If fruit cost $2.50 each and cookies cost $1.25 each, how many of each did you buy? 
Let number of fruit and cookies, be F and C, respectively

Then we get: F + C = 90 ----- eq (i)

Also, 2.5F + 1.25C = 125 ---- eq (ii)

            2F + C = 100 ---- Factoring out GCF, 1.25 in eq (ii) ----- eq (iii)

                 F = 10 ----- Subtracting eq (i) from eq (iii)

Number of fruit purchased, or F = 10.

Now, it's easy to find number of cookies purchased.