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Question 1015398: Ranjana's mother Gave her ₹245 for buying new year cards. If she got some 10 rupee cards 2/3 as many 5 rupee cards and 1/5 as many 15 rupee cards,how many of each kind did she buy?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of 10 rupee cards.
y = number of 5 rupee cards
z = number of 15 rupee cards.
total number of rupees is 245.
the number of 5 rupee cards is equal to 2/3 times the number of 10 rupee cards.
this says that y = 2/3 * x.
the number of 15 rupee cards is equal to 1/5 times the number of 10 rupee cards.
this says that z = 1/5 * x.
the total amount of money spent is 245 rupees.
the equation to represent this is:
10 * x + 5 * y + 15 * z = 245
since y = 2/3 * x and z = 1/5 * x, the equation becomes:
10 * x + 5 * 2/3 * x + 15 * 1/5 * x = 245
if you place everything on the left side of the equation over the common denominator of 15, then you get:
10 * 15/15 * x + 5 * 10/15 * x + 15 * 3/15 * x = 245
simplify to get 150/15 * x + 50/15 * x + 45/15 * x = 245
combine like fractions to get:
245/15 * x = 245
multiply both sides of this equation by 15/245 to get x = 245 * 15/245.
simplify to get x = 15.
when x = 15, y = 2/3 * x becomes y = 10 and z = 1/5 * x becomes z = 3.
your solution should b3e:
x = 15
y = 10
z = 3
you have 15 * 10 rupee cards equals a total value of 150 rupees.
you have 10 * 5 rupee cards equals a total value of 50 rupees.
you have 3 * 15 rupee cards equals a votal value of 45 rupees.
total value is 245 rupees.
this confirms the solution is good.
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