Math combinations?

Question

I need two combinations of these chocolates where the total cost equals $14.80.

Fudge centers: $0.60
Nut clusters: $0.75
Truffles: $0.80

i just wanted to say thank you to all the people that took the time to help me. thanx =)

Answer 1

you have .60F + .75N + .80T = cost, so
let F = 5, N = 8 and see what you've got:

.60(5) + .75(8) + .80T = 14.80
3 + 6 + .80T = 14.80
.80T = 5.80
T = 7.25

let F = 10, N = 4:
.60(10) + .75(4) + .80T = 14.80
6 + 3 + .80T = 14.80
.80T = 5.80
T = 7.25

Pick any values of 2 variables (that don't overshoot the total), and solve for the 3rd.

Answer 2

... Unfortunately, the fastest way to do this is brute force. But, we can make it easier:

F=Fudge centers
N=Nut clusters
T=Truffles

.6F + .75N + .8T = 14.8

... I find fractions easier than decimals, and whole numbers even easier...

3/5F + 3/4N + 4/5T = 14 + 4/5 = 74/5

... Solving for the smallest common denominator...

(12F + 15N + 16T)/20 = 296/20

12F + 15N + 16T = 296

... Values of N are the easiest to narrow...

12F + 16T = 296 - 15N

... For all whole values of F & T, the left side of the equation will always be divisible by 4, therefore the same must be true for the right. Since 296 is divisible by 4, and N is being multiplied by an odd number, all values of N that could solve this equation must either be 0 or be divisible by 4, limiting us to 0, 4, 8, 12, and 16. That leaves with 5 equations to solve for:

12F + 16T = 296 - 15(0) = 296
12F + 16T = 296 - 15(4) = 236
12F + 16T = 296 - 15(8) = 176
12F + 16T = 296 - 15(12) = 116
12F + 16T = 296 - 15(16) = 56

... Solving the last one will help give us pattern to solve the rest. By trial and error, if N=16, then F=2 & T=2. The difference in solving for N=16 & N=12 is 60, which so happens to be divisible by 12, so T=2 will work again for N=16; F will equal 7. Knowing that, the next smallest value of T that will work must be 3 more than the last, since 48 is the smallest multiple of 16 that is also a multiple of 12. So if N=12 & T=2+3=5, that leaves F=3. With this pattern continuing, here should be all possible answers:

N=16 T=2 F=2
N=12 T=2 F=7
N=12 T=5 F=3
N=8 T=2 F=12
N=8 T=5 F=8
N=8 T=8 F=4
N=8 T=11 F=0
N=4 T=2 F=17
N=4 T=5 F=13
N=4 T=8 F=9
N=4 T=11 F=5
N=4 T=14 F=1
N=0 T=2 F=22
N=0 T=5 F=18
N=0 T=8 F=14
N=0 T=11 F=10
N=0 T=14 F=6
N=0 T=17 F=2

... Pick any 2 answers you like...

Answer 3

Right assuming you need whole values of each...

we know that 14.80 doesn't end in 5 thus there are an even number of Nut Clusters, going further seeing .8 and knowing that 2*0.75=1.5 we can see that the number of nut clusters must be a multiple of 4 (because .6 and .8 are even and adding that to 1.5 we we never get x.8)

so lets start with 4 nut clusters that leaves 11.8 to distribute between the fudge centers and truffles.

Now we find the first multiple of both Truffles and Fudge Centers which 2.40, thus for 2.40 we can have 3 Truffles or 4 Fudge Centers.

subtract 2.40 from 11.80 the maximum number of times possible 4 in this case, which leaves 2.20, which we can divide up into 2*0.60 + 0.80.

thus summing up we have:

4 Nut Clusters,
1 Fudge Center,
2 Truffles,
4 packs of your choice 3 Truffles or 4 Fudge clusters

So now you can give 4 combinations.

There also exist other combinations using 8 Nut Clusters...

Answer 4

I have worked this all sorts of ways and you can't get the exact amount that I know of. You would have 4x 60+75=5.40 and 4x80+75= 6.20 and 3 x 80+60=4.20 which would total 15.80 so you would have to take one off and I would take one of the 60+75 of and you would have 14.45. so you have 10 or 11 combinations.

Answer 5

This is called problem solving. You are not solving the problem if you ask someone else to do it. Roll up your sleeves and get dirty. You will feel SO GOOD about it when you're done.

Answer 6

do you have to get each chocolate?? or can you just buy the fudge and teh truffles?

Answer 7

12 @ 0.60 = 7.20

8 @ 0.75 = 6.00

2 @ 0.80 = 1.60

Answer 8

.6x+.75y+.8z=14.8