j costs twice as much as b. b costs twice as much as k. all three letters together cost 17.50. what is the price of each letter?
b = 2k
j = 4k
k + 2k + 4k = 17.50
7k = 17.50
k = 17.50/7
k = 2.50
To solve this problem, we need to set up a system of equations based on the given information. Let's assign variables to the unknown prices.
Let's say the price of k is x. Therefore, the price of b would be twice x, and the price of j would be twice the price of b.
So, we have:
k = x
b = 2x
j = 2b = 2(2x) = 4x
Now, we know that the sum of their prices is $17.50, so we can write the equation:
k + b + j = 17.50
Substituting the values we found earlier:
x + 2x + 4x = 17.50
Now, we can solve for x:
7x = 17.50
x = 17.50/7
x ≈ 2.5
Hence, the price of k is approximately $2.50. Using this value, we can find the prices of b and j:
b = 2x = 2 * 2.5 = $5
j = 4x = 4 * 2.5 = $10
Therefore, the price of k is $2.50, the price of b is $5, and the price of j is $10.