Question

If a rectangular prism block of wood has dimension 7 cm * 5 cm * 4 cm and cost $40 , what is the fair price in dollars of a 14 cm * 20 cm * 24 cm block of the same type if price is determined solely by volume?

Answer 1

What have you attempted so far?

Answer 2

i know i need to set up a ratio but I do not know how.

Answer 3

Well do you know how to find the ratio of the volume of the bigger block to the smaller block?

Answer 4

No :(

Answer 5

For the big block you have: $$ 14 cm,~20 cm,~24 cm $$
For the small block you have: $$ 7 cm,~5 cm,~4 cm $$

Can you construct a ratio from this?

Answer 6

40: 7*5*4
40:140
4:14
0.286

x:14*20*24
x:6720
0.286 = x/6720
0.286(6720) = x
x = 1921

Answer 7

@kevin4762 what?

Answer 8

Hmm, I took a different approach to this.

The ratio of the volume of the big block to the smaller block is:
$$u1=2 \times 4 \times 6=48$$
Then the fair price is:
$$40 \times 48 = 1920$$

Answer 9

okay the ratio of price to wood is $40 for a rectangular prism of wood which has a volume of 140 units cubed.

So we need to determine a fair price for a rectangular prism of wood which has a volume of 6720 units cubed. The ratio of dollars to volume is 40:140 which is .286. If we solve for x to see what price will give us a ratio of .286 when the volume is 6720, then we get 1921.

Answer 10

Algorithmic's method is fine as well. There's always more than one way of solving a math problem. We both got approximately the same answer.

Answer 11

I like Kevin's method. More accurate. +1

Answer 12

oh i understand. thanks guys