Amount

[Guest]

Sand and gravel are combined in two different piles.

First pile; Sand mixed with gravel in 1:3 ratio.

Second pile; Sand mixed with gravel in 3:5 ratio.

Determine amount removed from each pile to combine in a third pile to contain 5 cu. yds. of sand and 9 cu. yds. of gravel.

Unsure how to solve.

[Baltuilhe]

Good night!

First pile:
1:3 ratio, so 1+3=4
1:4 of sand
3:4 of gravel

Second pile:
3:5 ratio, so 3+5=8
3:8 of sand
5:8 of gravel

Combined pile:
5:9 ratio, so 5+9=14
5:14 of sand
9:14 of gravel

Now LCD of denominators: LCD of 4, 8 and 14:
4=2^2
8=2^3
14=2 * 7
LCD(4,8,14)=2^3 * 7=8 * 7=56

So, choose a material and 'fix' the ratio using the LCD.
Sand, for instance:
(1:4)x + (3:8)y = (5:14)(x+y), right?
(14:56)x + (21:56)y = (20:56)(x+y)
14x+21y=20(x+y)
14x+21y=20x+20y
21y-20y=20x-14x
y=6x

So, proportion is 1 part of pile1 to 6 parts of pile 2. But you want 14 cubic inches (5 cubic inches of sand plus 9 cubic inches of gravel)
1 + 6 = 7, so, if you want 14, double the value
2 + 12 = 14, right?

2 cubic inches of pile1 + 12 cubic inches of pile2 has 5 cubic inches of sand and 9 cubic inches of gravel

2(1/4)+12(3/8)=1/2+9/2=10/2=5 cubic of sand
2(3/4)+12(5/8)=3/2+15/2=18/9=9 cubic of gravel

Hope to Have Helped (3H)

[Guest]

You have cu. in. in answer, but problem states cu. ft. I guess that would not make any difference.

[Baltuilhe]

Sorry for that!

No problems! Just a change of unit!

[Guest]

Good Afternoon!!

Ok, Thanks again.