Meatpacking plant sells two grades of steak, three dollars a pound for the lower
ID: 2896359 • Letter: M
Question
Meatpacking plant sells two grades of steak, three dollars a pound for the lower grade and six dollars a pound for the higher grade. One week, they sell a total of 400 pounds of steak for $1600 some to a fast food restaurant at the lower price and some to a higher and steak restaurant at the higher price. How much did each restaurant buy?
The next week, they put their steaks on sale, with the low-grade price dropping to $2.75 a pound in the higher great price dropping two $5.25 a pound. How much did each restaurant by this week it's a total amount was 600 pounds for $2000?
Explanation / Answer
In the first week, let x lbs be the quantity of lower grade meat sold to the fast food restaurant at $ 3 per lb and let y lbs be the quantity of higher grade meat sold to the high end restaurant at $ 6 per lb.Then, we have
x + y = 400 .....(1) and
3x + 6y = !600....(2)
On multiplying both the sides of the 1st equation by 3 and reducing it from the 2nd equation, we have, 3x + 6y - (3x + 3y) = 1600 - 3*400 or, 3y = 400. Therefore y = 400/3lbs = 133.33lbs ( on rounding off to 2 decimal places)
Now, from the 1st equation, we have x = 400 -y = 400- 400/3 = 800/3 lbs = 266.67 lbs ( on rounding off to 2 decimal places). We can verify the result by substituting the values of x and y in the 2nd equation.
In the next week, let a lbs be the quantity of lower grade meat sold at $ 2.75 per lb and let b lbs be the quantity of higher grade meat sold $ 5.25 per lb.Then, we have
a + b = 600....(3) and
2.75a + 5.25b = 2000...(4)
On multiplying both the sides of the 2nd equation by 4 ( to get rid of the decimals), we have
11a + 21b = 8000 ....(5)
Now, on multiplying both the sides of the 3rd equation by 11 and reducing it from the 25th equation, we have,
11a + 21b - (11a+11b) = 8000- 11*600 or, 10b = 1400 or, b = 140 lbs. Then from the 3rd equation, we get a =600 - b = 600 -140 = 460 lbs
We can verify the result by substituting the values of a and b in the 5th equation.