4 plates and 3 cups cost 15.40 dollars. 5 plates and 4 cups cost 19.60 dollars. Each plate costs the same amount as the other plates, and each cup costs the same amount as the other cups. What is the cost of 1 plate? What is the cost of 1 cup?
Answers
Given:
4 plates and 3 cups cost 15.40 dollars. 5 plates and 4 cups cost 19.60 dollars. Each plate costs the same amount as the other plates, and each cup costs the same amount as the other cups.
To find:
What is the cost of 1 plate? What is the cost of 1 cup?
Solution:
Let,
"p" → be the cost of 1 plate
"c" → be the cost of 1 cup
As given in the question, we can form the equations as:
4p + 3c = 15.40 . . . . (1)
and
5p + 4c = 19.60 . . . . (2)
On multiplying equation (1) by 5 and equation (2) by 4, we get
20p + 15c = 77 . . . . (3)
and
20p + 16c = 78.40 . . . . (4)
On subtracting equation (3) from (4), we get
20p + 16c = 78.40
20p + 15c = 77
- - -
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c = 1.4
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On substituting the value of c in equation (1), we get
4p + 3(1.4) = 15.40
⇒ 4p + 4.2 = 15.40
⇒ 4p = 11.2
⇒ p = 2.8
Thus,
The cost of 1 plate is → 2.80 dollars
The cost of 1 cup is → 1.40 dollars
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