word problem- application problem

[marko]

Here is a word problem. A health food store combines cranberry juice that cost $2.79 per quart with apple juice that costs $2.19 per quart. How many quarts of each were used to make 10 quarts of a cranapple juice mixuter that costs $ 2.31 per quart? I know many word problems throw a monkey wrench into the mix. Does the new price of the juice even have a relivence to the problem?

 

[stapel]

Use the standard "mixture" formulation:

. . .quarts juice:
. . . . .cran: c
. . . . .apple: 10 - c
. . . . .mix: 10

. . .cost per quart:
. . . . .cran: 2.79
. . . . .apple: 2.19
. . . . .mix: 2.31

. . .total cost:
. . . . .cran: 2.79c
. . . . .apple: ??
. . . . .mix: ??

Complete the table. Add the input costs, set equal to the total cost, and solve.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[TchrWill]

Here is a word problem. A health food store combines cranberry juice that cost $2.79 per quart with apple juice that costs $2.19 per quart. How many quarts of each were used to make 10 quarts of a cranapple juice mixuter that costs $ 2.31 per quart? I know many word problems throw a monkey wrench into the mix. Does the new price of the juice even have a relivence to the problem?

Letting x and y be the desired quantities:
We know that 219x + 279y = 2310.
We also know that x + y = 10
I suspect you can take it from here.

 

[marko]

word problem - application problem

Well, yes I see that 2310 is that part of the problem, but that still does not tell me how much of each juice was used to make up ten gallons. :?:

 

[stapel]

Well, yes I see that 2310 is that part of the problem, but that still does not tell me how much of each juice was used to make up ten gallons.

You were given explanations and the set-up. No, you have not been provided with the complete solution; you were left with a step or two to do yourself.

Did you follow the instructions provided by either of the above replies? If not, please do so now. If so, please reply showing all your steps.

Thank you.

Eliz.

 

[TchrWill]

Here is a word problem. A health food store combines cranberry juice that cost $2.79 per quart with apple juice that costs $2.19 per quart. How many quarts of each were used to make 10 quarts of a cranapple juice mixuter that costs $ 2.31 per quart? I know many word problems throw a monkey wrench into the mix. Does the new price of the juice even have a relivence to the problem.

Letting x and y be the desired quantities of apple and cranberry juice respectively.:
We know that 219x + 279y = 2310.
We also know that x + y = 10
Multiply the second by 219 and subtract from the first yielding 60y = 120 making y = 2 quarts of apple juice and x = 8 quarts of cranberry juice.

[2.19(8) + 2.79(2)]/10 = $2.31/quart pf the 10 quart mixture.

 

[marko]

word problem-application problem

Chart


c Amt cost value

cran c 2.79 2.79c

apple 10-c 2.19 2.19 (10-c)

mix 10 2.31 2.31(10)

2.79c + 2.19(10-c) = 2.31 (10)
2.79c +21.90 -2.19c = 23.10
.60c + 21.90 = 23.10
.60c +21.90-21.90 = 23.10 -21.90
.60c = 1.20
c = 2 is this 2 gallons of cranberry juice?
If this is the case then the apple juice is 8 gallons???

 

[stapel]

c = 2 is this 2 gallons of cranberry juice?

This is why it is important to thoroughly read the question, and to label the variables: so that, at the end, you know what "c" stands for.

(Hint: The question is stated in terms of "quarts".)

If this is the case then the apple juice is 8 gallons?

"Eight gallons" (that is, thirty-two quarts) seems unlikely.

It should be noted that the answer to any "solving" exercise may be checked by plugging it back into the initial problem. In this case, if you have two units of something at $2.79 per unit, and eight units of something else at $2.19 per unit, does this sum to the same value as ten units at $2.31 per unit?

Plug your numbers in and check.

Eliz.

 

[TchrWill]

Marko wrpte:

c = 2 is this 2 gallons of cranberry juice?
If this is the case then the apple juice is 8 gallons???

Let's assume that Marko momentarily got confused and stated gallons instead of quarts as originally stated.

Marko, if you got 2 and 8 as the quantities, the units are still quarts as stated in the original problem.

 

[marko]

word problem-application problem

Yes, I momentarily lost my thought, as someone was pounding on my front door. Sorry. I meant quarts. Thanks. marko