Ben, Jerry and Kumar had some flour. The ratio of the amount of flour Ben had to the amount of flour Jerry had was 2:3. Jerry had 4/5 the amount of flour Kumar had. Kumar had 420 g of flour more than Ben. How much flour did Jerry have?

Question

Ben, Jerry and Kumar had some flour. The ratio of the amount of flour Ben had to the amount of flour Jerry had was 2:3. Jerry had 4/5 the amount of flour Kumar had. Kumar had 420 g of flour more than Ben. How much flour did Jerry have?

1) 240 g
2) 630 g
3) 720 g
4) 840 g

Answer 1

B/J = 2/3

J/K = 4/5
K = B + 420

well B= 2 J / 3
and K = 5 J/4
so
5 J / 4 = 2 J / 3 + 420
15 J / 12 - 8 J / 12 = 420
7 J = 420 * 12
J = 720

Answer 2

Let's break down the information given step by step:

1. The ratio of the amount of flour Ben had to the amount of flour Jerry had was 2:3.
2. Jerry had 4/5 the amount of flour Kumar had.
3. Kumar had 420 g of flour more than Ben.

Let's assign variables to represent the unknown amounts of flour:
Let B represent the amount of flour Ben had.
Let J represent the amount of flour Jerry had.
Let K represent the amount of flour Kumar had.

Based on the first piece of information, we can set up the equation:
B/J = 2/3

Based on the second piece of information, we can set up the equation:
J = (4/5)K

Based on the third piece of information, we can set up the equation:
K = B + 420

We can solve this system of equations to find J.

First, let's substitute K in terms of B into the equation for J:
J = (4/5)(B + 420)

Next, substitute J into the equation B/J = 2/3:
B/[(4/5)(B + 420)] = 2/3

Now, cross-multiply and solve for B:
3B = 2[(4/5)(B + 420)]
3B = (8/5)(B + 420)
15B = 8B + 3360
7B = 3360
B = 480

Now, substitute the value of B back into the equation K = B + 420 to find K:
K = 480 + 420
K = 900

Finally, substitute the values of B and K into the equation J = (4/5)K to find J:
J = (4/5)(900)
J = 720

Therefore, Jerry had 720 g of flour. So the correct answer is option 3) 720 g.

Answer 3

To find out how much flour Jerry had, we need to analyze the given information step by step.

Let's assign variables to the unknown quantities:
Let the amount of flour Ben had be B.
Let the amount of flour Jerry had be J.
Let the amount of flour Kumar had be K.

Based on the given information, we have the following relations:
1) The ratio of the amount of flour Ben had to the amount of flour Jerry had was 2:3:
B/J = 2/3

2) Jerry had 4/5 the amount of flour Kumar had:
J = (4/5)K

3) Kumar had 420 g of flour more than Ben:
K = B + 420

Now, we can solve these equations to find the value of J.

First, let's eliminate the variable K. From equation 3, we can substitute the value of K in equation 2:
J = (4/5)(B + 420)

Next, let's substitute the value of J from equation 1 into the above equation:
B/(2B/3) = (4/5)(B + 420)

To simplify the equation, multiply both sides by (2B/3):
B = (2/3)(4/5)(B + 420)

Next, simplify the right side of the equation:
B = (8/15)(B + 420)

Expand the right side:
B = (8/15)B + (8/15)(420)

Combining like terms:
B - (8/15)B = (8/15)(420)

Simplify the left side of the equation:
(7/15)B = (8/15)(420)

Divide both sides by (7/15) to solve for B:
B = (8/15)(420) / (7/15)

Solve the right side of the equation:
B = 8 * 420 / 7

B = 480

Now that we know the value of B, we can find the value of J using equation 1:
B/J = 2/3

Substitute the value of B as 480:
480/J = 2/3

Cross multiply:
3 * 480 = 2J

1440 = 2J

Divide both sides by 2 to solve for J:
J = 1440 / 2

J = 720

Therefore, Jerry had 720 g of flour.

So, the correct answer is 3) 720 g.