Final answer:
To find the total cost of the watch and the clock, set up equations based on the given relationships, solve for the individual costs, and then add them together. The total cost amounts to $176.
Step-by-step explanation:
The student is asking to find the total cost of two items - a watch and a clock. The clock costs 4/7 of what the watch costs, and the watch costs $48 more than the clock. Let's denote the cost of the clock as c and the cost of the watch as w. The problem gives us two equations: w = c + $48 and c = (4/7)w. Now, we can solve these equations to find the individual costs of the clock and the watch, then sum them to find the total cost.
Step-by-step Solution
Substitute the value of c from the second equation into the first equation: w = (4/7)w + $48.
Multiply both sides of the equation by 7 to eliminate the fraction: 7w = 4w + $336.
Subtract 4w from both sides: 3w = $336.
Divide both sides by 3 to find the cost of the watch: w = $112.
Now that we have the cost of the watch, we can substitute it back into the equation c = (4/7)w to find the cost of the clock: c = (4/7) x $112 = $64.
The total cost of both items is the sum of the cost of the clock and the cost of the watch: w + c = $112 + $64 = $176.
Therefore, the total cost of the watch and the clock together is $176.