The total cost of 2 identical cups, 3 identical plates and 1 bowl is $116. The total cost of 3 such plates and the bowl is $64. The cost of 1 cup is twice as much as the cost of 1 plate. What is the total cost of the 3 plates?
c = 2p
3p+b = 64
2c+3p+b = 116
so 3p = $39
Let the cost of cups = c
Let the cost of plates = p
Let the cost of bowl = b
Equation 1
2c + 3p = 1b = $116
Equation 2
3p + 1b = $64
Equation 3
1c = 2p
* In equation 2
3p + 1b = $64
1b = $64 - 3p
b = $64 - 3p
* Substitute; equation 3 and equation 2 in equation 1
Equation 1: 2c + 3p + b = $116
2 (2p) + 3p + ($64 - 3p) = $116
4p + 3p - 3p = $116 - $64
4p/4 = $52/4
p = $13
The cost of one plate is $13
Total cost of 3 plates = $13 * 3 = $39
To find the total cost of the 3 plates, we need to determine the cost of each plate first.
Let's assume the cost of one plate is "P" dollars. According to the given information, the cost of one cup is twice as much as the cost of one plate. Therefore, the cost of one cup is "2P" dollars.
From the first statement, we know that 2 identical cups, 3 identical plates, and 1 bowl together cost $116. Using this information, we can set up an equation:
2(2P) + 3P + 1B = $116
Simplifying the equation, we have:
4P + 3P + 1B = $116
7P + 1B = $116
From the second statement, we know that the total cost of 3 plates and the bowl is $64. We can set up another equation using this information:
3P + 1B = $64
Now we have a system of equations:
7P + 1B = $116
3P + 1B = $64
To solve this system, we can subtract the second equation from the first equation, which will eliminate the "B" term:
(7P + 1B) - (3P + 1B) = $116 - $64
7P - 3P + 1B - 1B = $52
Simplifying the equation, we get:
4P = $52
Dividing both sides by 4, we find:
P = $13
Therefore, the cost of one plate is $13.
To find the total cost of the 3 plates, we multiply the cost of one plate by 3:
Total cost of 3 plates = 3P = 3 * $13 = $39
Hence, the total cost of the 3 plates is $39.