Need Help !!!

Question

The ratio of lime to mortar is 3:7. How much lime must be mixed with 21 bags of sand to make mortar?

Answer 1

There are 2 ways to solve this problem:

 

Option 1:

Multiply across

3/7= ?/21      7*3=21     so 3*3=?  (9 limes)

 

Option 2:

Cross multiplication

3/7=?/21       21*3=63   so 63/7=? (9 limes)

Answer 2

The ratio of 3:7 is not the ratio of lime to sand, but lime to mortar. 

 

Let the amount of lime be L, and the amount of sand be S.  The amount of mortar is L + S.

 

The equation is then

L/(L+S) = 3/7.  We need to solve for L.  Substitute in the value S = 21:

L/(L+21) = 3/7.  Cross-multiply:

7L = 3(L+21).  Distribute the 3:

7L = 3L + 63.  Subtract 3L from both sides:

4L = 63.  Divide both sides by 4:

L = 63/4.

 

The answer is not as pretty, but it follows from a precise reading of the problem statement.

 

Answer 3

 

Yes, agreed.  3/7 = x/21  cross multiplication is best, or mental math if you know how many 7's go into 21...whatever you multiply across on the bottom, you must also be fair and do the same to the top!  ;)