How many pounds of red grapes worth .95 per pound do you need to mix with green grapes worth 1.25 per pound to have a mixture of 12 pounds of grapes worth $1.15 per pound??????????
I can't figure this out and its worth extra credit
Thank you!!!!!!!
kelliegirl33
r + g = 12 --> r = 12 - g
.95r + 1.25g = 12(1.15)
now sub 12 - g in for r in the 2nd equation...
.95r + 1.25g = 12(1.15)
.95(12 - g) + 1.25g = 13.8
11.4 - .95g + 1.25g = 13.8
.30g = 13.8 - 11.4
.30g = 2.4
g = 2.4/.30
g = 8
now sub 8 in for g in either of the original equations...
r + g = 12
r + 8 = 12
r = 12 - 8
r = 4
you will need 4 lbs. of red grapes which equals (4 x .95) = 3.80
you will need 8 lbs of green grapes which equals (8 x 1.25) = 10.00
add together and you get 12 lbs at 13.80. Now divide 13.80 by 12 = 1.15 per pound.
IceHot
Pounds of red grapes = y
Pounds of green grapes = (12-y)
Cost of red grapes = 0.95 * y
Cost of green grapes = 1.25 * (12-y)
Total cost of grapes = 12 * 1.15 = 13.8
0.95y + 1.25 (12-y) = 13.8
0.95y + 15 - 1.25y = 13.8
15 - 0.3 y = 13.8
- 0.3y = 13.8 - 15
- 0.3 y = -1.2
3y = 12
y = 4
Pounds of red grapes = y = 4
Pound of green grapes = (12-y) = 8
Battleaxe
1) r + g = 12 or r = 12 - g
2) 95r + 124g = 115(12)
substitute equation(1) into equation(2):
95(12 - g) + 124g = 1380
1140 - 95g + 124g = 1380
29g = 240
g = 240/29 = 8.3 pounds
using equation(1):
r = 12 - 8.3 = 3.7 pounds
check using equation(2):
95(3.7) + 124(8.3) = 1380
351.5 + 1029.2 = 1380
1380.7 = 1380 due to rounding
Mix 3.7 pounds of red grapes and 8.3 pounds of green grapes.
- .--
Anonymous
r = lb's of red grapes
g = lb's of green grapes
r + g = 12
.95r + 1.25g = 12 x $1.15
.95r + 1.25(12-r)= $13.80
.95r - 1.25r +15 = $13.80
-.30r = -$1.20
r = 4lb
4lb + g= 12
g = 8lb
Check:
4lb x .95 + 8lb x 1.25 = $13.80