He had 15 of 8 cents stamps, 10 of 30 cents stamps and 20 of 6 cents stamps
Step-by-step explanation:
Daniel has a collection of stamps
The collection worth $6
He has five more 8 cents stamps than 30 cents stamps
The number of 6 cents stamps is twice the number of 30 cents stamps
The number of 5 cents is twelve
We need to find how many of each kind of stamps he had
Assume that the number of 8 cents stamps is x, the number of 30 cents stamps is y and the number of 6 cents stamps is z
∵ There are x of 8 cents stamps
∵ There are y of 30 cents stamps
∵ He has five more 8 cents stamps than 30 cents stamps
- That means y is less than x by 5
∴ y = x - 5 ⇒ (1)
∵ There are y of 6 cents stamps
∵ The number of 6 cents stamps is twice the number of
30 cents stamps
- That means equate z by 2y
∴ z = 2y ⇒ (2)
- Substitute y by equation (1)
∵ z = 2(x - 5)
∴ z = 2x - 10 ⇒ (3)
∵ There are 12 of 5 cents stamps
∴ Daniel's collection has x + y + z + 12 stamps
∵ Daniel's collection of stamps worth $6
- Change the dollars to cents
∵ 1 dollar = 100 cents
∴ $6 = 6 × 100 = 600 cents
- Multiply x by 8, y by 30, z by 6 and 12 by 5 to find the values
of all stamps and equate their sum by 600
∵ 8x + 30y + 6z + 12(5) = 600
∴ 8x + 30y + 6z + 60 = 600
- Subtract 60 from both sides
∴ 8x + 30y + 6z = 540 ⇒ (4)
Substitute y by equation (2) and z by equation (3) in equation (4)
∵ 8x + 30(x - 5) + 6(2x - 10) = 540
- Simplify the left hand side
∴ 8x + 30x - 150 + 12x - 60 = 540
- Add like terms
∵ (8x + 30x + 12x) + (-150 - 60) = 540
∴ 50x - 210 = 540
- Add 210 from both sides
∴ 50x = 750
- Divide both sides by 50
∴ x = 15
- Substitute the value of x in equation (1) and (3) to find y and z
∵ y = 15 - 5
∴ y = 10
∵ z = 2(15) - 10
∴ z = 30 - 10
∴ z = 20
He had 15 of 8 cents stamps, 10 of 30 cents stamps and 20 of 6 cents stamps
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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