How do you solve this word problem?

Question

three seizes of soft drinks are sold at a festival. the large (24 oz) is sold for $3, the medium (16 oz) for $2 and the small (10 oz) for $1.50 A total of 530 are sold, bringing in a total of $1,135. If a total of 8, 660 oz of soft drink was sold, how many large drinks were dold?

Answer 1

Make three equations.
Using the first letters to represent the number sold of the different drink sizes:

L + M + S = 530 = total drinks sold
24L + 16M + 10S = 8660 = total ounces of soft drink sold
3L + 2M + 1.5S = 1135 = total amount of money taken in

Looking for relationships among the numbers in the equations, it looks like we can start with the second and third equations because 3 times 8 is 24 and 2 times 8 is 16. Maybe we can get rid of some of the variables.

24L + 16M + 10 S = 8660 Now multiply the 3rd equation's terms by 8.
24L + 16M + 12S = 1135*8=9080 Subtract the second equation from this modified third equation.
2S = 9080-8660
2S = 420
S = 210

Now we can substitute 210 for S in any equation.
I'm going to work with the first and third original equations because who wants to mess with 24s when we could be using 1 and 2?
L + M + 210 = 530
3L + 2M + 315 = 1135 Simplify the two equations.

L + M = 320
3L + 2M = 820 Multiply first equation by 2 to get rid of M.
2L + 2M = 640 Subtract equations.
L = 180

L is the one that answers the question.
180 large drinks were sold.

Check:
180 large and 210 small + M medium = 530
M = 140

Money taken in
180*3 + 140*2 + 210*1.5 = 1135
540 + 280 + 315 = 1135
1135 = 1135

Correct.

Answer 2

Pickin' nits, tj?
x + y + z = 530
24x + 16y + 10z = 8,660
3x + 2y + 1.5z = 1,135
3x + 3y + 3z = 1,590
y + 1.5z = 455
24x + 24y + 24z = 12,720
24x + 16y + 10z = 8,660
8y + 14z = 4060
8y + 12z = 3640
2z = 420
z = 210 small drinks
y = 455 - 1.5*210
y = 140 medium drinks
x = 530 - 140 - 210
x = 180 large drinks

Answer 3

180 large drinks were sold

let x : number of 24 oz drinks
y : number of 16 oz drinks
530 - x - y : number of 10 oz drinks

you have a system of 2 equations:

(this one is based on ounces and number of drinks)
24x + 16y + 10(530 - x - y) = 8660

and

(this one is based on prices and number of drinks)
3x + 2y + 1.5(530 - x - y) = 1135

so:
24x + 16y + 10(530 - x - y) = 8660
24x + 16y + 5300 - 10x - 10y = 8660
14x + 6y + 5300 = 8660
14x + 6y = 3360

3x + 2y + 1.5(530 - x - y) = 1135
3x + 2y + 795 - 1.5x - 1.5y = 1135
1.5x + 0.5y + 795 = 1135
1.5x + 0.5 y = 340

eliminate y:
14x + 6y = 3360
-12 (1.5x + 0.5 y = 340)
---------------------------------

14x + 6y = 3360
-18x - 6y = -4080
----------------------------
-4x = -720
x = 180

bonus complete solution:

find y if x = 180:
1.5(180) + 0.5 y = 340
270 + 0.5y = 340
0.5y = 70
y = 140

so:
530 - x - y
= 530 - 180 - 140
= 210

so:
180 units of 24-oz drinks at $3 each were sold
140 units of 16-oz drinks at $2 each were sold
210 units of 10-oz drinks at $1.50 each were sold

Answer 4

Set A=large size, $3, 24oz
B=medium size, $2, 16oz
C=small size, $1.50, 10oz

Total = A + B + C = 530

Cash = 3A + 2B + 1.5C = 1135

Oz = 24A + 16B + 10C = 8660

Solve for the variables.

Answer 5

particular you may label the variable x as width and length could be x + 12 make an equation 2x + 2(x+12) = 156 for the reason which you upload all facets to get perimeter then u clean up for x yielding the respond x = 33 = width x + 12 = 40 5 = length

Answer 6

L+M+S=530
3L+2M+1.5S=1135
24L+16M+10S=8660

3 unknowns and 3 equations, you can solve it now . . .

Answer 7

"drinks were DOLD?"

The answers is yes.

Answer 8

lack of data