Question

1/2 lb of fish costs twice as much as 4/5 lb of vegetables. If 7/10 lb of fish and 1/2 lb of vegetables cost $13.70 altogether, how much more does each lb of fish cost than each lb of vegetables?

a) $4.50
b) $5.00
c) $4.00
d) $3.50

Answer 1

This high school level mathematics question involves solving a system of equations to find out the difference in cost per pound between fish and vegetables.

Step-by-step explanation:

The subject of the question is Mathematics, and it pertains to ratio and proportion, unit price comparison, and algebra. We have been given that 1/2 lb of fish costs twice as much as 4/5 lb of vegetables. Our first equation from that statement is: 2V = F, where V is the cost per pound of vegetables and F is the cost per pound of fish. Then we are told that 7/10 lb of fish and 1/2 lb of vegetables cost $13.70 in total. This gives us our second equation: (7/10)F + (1/2)V = 13.70. By substituting 2V for F from the first equation into the second equation, we solve for V and then for F. After finding the individual prices per pound for fish and vegetables, we can then find the difference in cost per pound between the two.

During the solution process, it may be necessary to use some basic algebraic manipulation such as multiplying by a common denominator or isolating variables to solve the system of equations. Once we have the prices per pound for fish and vegetables, we subtract the cost per pound of vegetables from the cost per pound of fish to determine the difference in price between the two items, which will be our final answer.