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Question

How many combinations of 8 cent and 15 cent postcards can be purchased by spending
exactly $4.80? List each combination.

Answer 1

You could list out the various combinations, but a little thought reduces the number of combinations to try considerably. Let x be the number of 8 cent postcards and let y be the numberof 15 cent postcards.

We want to find x and y so that 0.08x + 0.15y = 4.80. That is (multiplying through by 100) 8x + 15y = 480 or (solving for y) y = 32 - (8/15)x

Since both x and y have to be integers, x must be a multiple of 15. But x can't be more than 60 since 60*8 = 480. so the possible values for x are: 0, 15, 30, 45 and 60. You can then plug these values into your equation for y to determine what y should be:

x = 0 implies y = 32
x = 15 implies y = 32 - 8 = 24
x = 30 implies y = 32 - 16 = 16
x = 45 implies y = 32 - 24 = 8
x = 60 implies y = 32 - 32 = 0

Math Rules!

Answer 2

If x = # of 8 cent cards, and y = # of 15 cent cards, then the combinations are as follows:

x=60, y=0
x=45, y=8
x=30, y =16
x=15, y=24
x=0, y=32

Answer 3

15x + 8y = 480
8y = 480 - 15x
y = (480 - 15x) / 8 = 60 - (15/8)x

So...
x must be a multiple of 8 in order for this equation to give you an integer answer.

If
x = 0, then y = 60
x = 8, then y = 45
x = 16, then y = 30
x = 24, then y = 15
x = 32, then y = 0

So... There are a total of 5 combinations. If you are required to have at least one of each kind of postcard, the answer is 3 combinations.

Answer 4

let number of 8 cents be x
number of 15 cents be y
nouw 8x+15y=480

now y cant be odd as then sum will be odd hence y is even
and when y is even ...15y is multiple of 30 and 480 is also a multiple 30 ....8x should be a multiple of 30 but thats only possible unless x is 0

so only cases come are when one of x or y is zero
that is
1) 0 8 cents and 32 15 cents
2) 0 15 cents and 60 8 cents

Answer 5

I used an excel chart listing all possible combinations and found the ones that equaled $4.80. Here are the results (with results listed as (# of $0.08, # of $0.15)):

(0, 32) (15, 24) (30, 16) (45, 8) (60, 0)

Answer 6

We have .08x + .15y = 4.80.

Multiply through by 100

8x + 15y = 480
This is a linear diophantine equation.

GCD of 8 and 15 is 1.
A particular solution is x = 60, y = 0.
All solutions are then given by:
x = 60 + 15n
y = 0 - 8n
where n is an integer.

So only solutions are:
(0, 28), (15, 24), (30, 16), (45, 8), (60, 0)

Answer 7

08 | 15

. 0 | 32
15 | 24
30 | 16
45 | 08
60 | 00