Given: John goes to the supermarket to get some juice cartons for the upcoming weekend party at his house. At the supermarket there are two types of juices available - Mango and Cranberry. A carton of mango juice costs $0.43 and a carton of cranberry juice costs $0.53.
Asked: In how many ways can John spend all $25 to buy juice cartons?

Let the number of cartons of mango juice be M and number of cartons of cranberry juice be C

.43M+.53C=25.00
43M+53C=2500
43(M+C)+10C=2500
M+C=10k format since last digit has to be 0
Let M+C=10
430+10C =2500 NOT FEASIBLE since M+C>C
Let M+C=20
860+10C =2500 NOT FEASIBLE since M+C>C
Let M+C=30
1290+10C =2500 NOT FEASIBLE since M+C>C
Let M+C=40
1790+10C =2500 NOT FEASIBLE since M+C>C
Let M+C=50
2150+10C =2500
C=35, M=15
FEASIBLE since M+C>C
Let M+C=60
2580+10C =2500 NOT FEASIBLE since C>0

Only one solution when C=35, M=15 is feasible

IMO B
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There is one solution available as shown above.

Posted from my mobile device
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43 and 53 are both prime.

The LCM of both is 2279. (43*53)

And we have to spend 2500.

So that is the only way possible.

Is this a correct approach?
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