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Help ASAP.

 

1) Every sack of sugar has the same weight. Every sack of flour has the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that three sacks of sugar together with four sacks of flour weighs no more than 50 kg, and that the weight of two sacks of flour is no more than 13 kg more than the weight of three sacks of sugar. What is the largest possible weight (in kg) of a sack of flour?

 

2) The sUpEr CoOl ReStAuRaNt offers two platters. Platter A comes with 4 hamburgers, 3 hot dogs, and 2 p*g's feet, and costs $15. Platter B comes with 3 hamburgers, 4 hot dogs, and 5 p*g's feet, and costs $12.

A picnic organizer requires 220 hamburgers, 270 hot dogs, and 250 p*g's feet. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost?

HelpPls  Nov 10, 2018
 #1
avatar+2793 
+2

\(3s + 4f \leq 50\\ 2f \leq 13+3s\)

 

\(4f \leq 50 - 3s\\ 2f \leq 13+3s \\ \text{add both inequalities}\\ 6f \leq 63\\ f \leq \dfrac{63}{6} = \dfrac{21}{2}\)

Rom  Nov 10, 2018
 #2
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+1

2)

I will give this a go!
Platter A costs $15 for 9 items or $15/9 =$1.67 per item
Platter B costs $12 for 12 items or $12/12=$1 per item
Since they need: 220 + 270 + 250 =740 items at a minimum, then they would need to buy: 740 / $12 =~62 platters B.
But 62 platters B will buy:
62 x 3 =186 hamburgers - 220 = -34 hamburgers short
62 x 4 =248 hot dogs -270 =-22 hot dogs short
62 x 5 =310 p*g's feet - 250 =60 pigs' feet left-over
Since the greatest shortage is 34 hamburgers, it therefore follows that 34/3 =12 additional B platters for a total:
62 + 12 = 74 platters B x $12 =$888 - the minimum cost.
This will give them:
74 x 3 =222 - with 2 hamburgers- left-over.
74 x 4 =296 - with 26 hot dogs-left-over.
74 x 5 =370 - with 120 pigs' feet-left-over.
And that is my attempt at this! Somebody should definitely take a second look at this!.

Guest Nov 10, 2018
 #3
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+1

The following breakdown is slightly cheaper:

 

7 platters A  x  $15 = $105

65 platters B  x  $12 =$780

$780 + $105 =$885

This will give them:

7 x 4 + 65 x 3 =223 hamburgers - with 3 leftover

7 x 3  +65 x 4 =281 hot dogs - with 11 leftover.

7 x 2 + 65 x 5 =339 pigs' feet - with 89 leftover.

Guest Nov 10, 2018
 #4
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+1

Here is YET a cheaper breakdown:

 

10 platters A  x  $15 =$150

60 platters B  x  $12 =$720

$150 + 720 =$870

This will give them:

10 x 4 + 60 x 3 =220 hamburgers - with no leftover

10 x 3 + 60 x 4 =270 hot dogs - with no leftover.

10 x 2 + 60 x 5 =320 pigs' feet - with 70 lefover.

Guest Nov 10, 2018
 #5
avatar+2793 
+1

(A,B) = (10,60) is the correct answer

Rom  Nov 10, 2018

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