Question

Part 1

The ratio table shows the amounts of sand and water in a concrete mixture. Which fraction represents the ratio for the gallons of water to bags of sand?
A)3/6
B)3/7
C)5/3
D)7/3
Part 2
How many bags of sand should be mixed with 12 gallons of water?
A)22 bags
B)24 bags
C)28 bags
D)30 bags
Please help

Answer 1

A)
`(3)/(7)`

C) 28 bags

Explanation:

Part 1 :

By the given table,

`\frac{\text{Gallon of water}}{\text{bags of sand}}=(6)/(14)=(9)/(21)=(15)/(35)=(3)/(7)`

Hence, the proportion of gallons of water to bags of sand is same,

Which is
`(3)/(7)`

OPTION A) is correct.

Part 2 : Let x bags of sand should be mixed with 12 gallon of water,

Then the ratio of gallon of water and number of bags of sand =
`(12)/(x)`

By part 1,

`(12)/(x)=(3)/(7)`

`84 = 3x` ( by cross multiplication )

`\implies x = (84)/(3)=28`

Hence, 28 bags of sand should be mixed.

OPTION C) is correct.

Answer 2

Divide bags of sand by gallons of water:

14 /6 = 2.33

21/9 = 2.33

The ratio is the same, so this means for every gallon of water you need 2.33 bags of sand.

Convert the fractions into decimals and you will get 7/3 = 2.33

The answer for Part 1 is D) 7/3

For part 2, multiply the gallons of water by 2.33 to get the number of sand bags needed:

12 x 2.33 = 27.99, which rounds to 28.

The answer is C) 28 bags.