Need done in 6 hrs !!!! plzhelp

Question

1.A bucket of sand has a mass 3 times the mass of a bucket of water. To make the mass of both buckets the same, megan removed 18 kilograms of sand from the sand bucket . What was the mass of the bucket7 of sand before the sand was removed? 

 

Show your work 

 

 

2.Fiona bought five carrots and seven potatoes for $4.10. Each carrot cost 10 cents more than a potato.  How much does a carrot cost ? 

 

Show your work

 

3. A mother is presently four times as old as her daughter. The sum of their ages six years ago was 48. Find their present ages.

 

Show your work

 

 

Answer 1

Let's look at problem 3.

 

If the daughter's age = x

Mom's age = 4x

 

Six years ago, the daughter's age is x - 6, and the mom's age is 4x - 6

 

(x - 6) + (4x - 6) = 48

5x - 12 = 48

5x = 60

x = 12 = daughter's age

 

Mom's age = 4x = 4 * 12 = 48

 

For problem 2, let x = price of potatoes, then (x + .10) = price of carrots

 

5(x + .10) + 7x = 4.10

5x + 0.5 + 7x = 4.10

12x + 0.5 = 4.10

12x = 3.60

x = 0.30 = 30 cents = price of potatoes

 

The price of carrots = x + .10 = .30 + .10 = .40 = 40 cents

 

Finally, for problem 1, let x = the mass of the bucket of water, then 3x = the mass of the bucket of sand

 

If we remove 18 kg of sand to make the two buckets equal in mass, then 

 

3x - 18 = x

2x - 18 = 0

2x = 18

x = 9 kg = mass of bucket of water

 

The mass of the bucket of sand is 3 * 9 = 27 kg