SOLUTION: a family consisting of three adults and five childrens spend in food Rs36 a week. Distress, however comes when they can afford only Rs 21 per week, and the food of each adult is di

Question 1054997: a family consisting of three adults and five childrens spend in food Rs36 a week. Distress, however comes when they can afford only Rs 21 per week, and the food of each adult is diminished by one half and each of child by one third. Find the cost per week of a child and adult?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the cost of one meal for one adult.
let y equal the cost of one meal for one child.

there are 3 adults and 5 children.
the total cost = 36.

your first equation is 3x + 5y = 36

when the family can only afford 21 per week, they reduce the adult portion by 1/2 and they reduce the child portion by 1/3.

each adult therefore gets 1/2 their normal portion and each child gets 2/3 their normal portion.

since the cost of the food hasn't changed, then the cost per adult becomes 1/2 * x and the cost per child becomes 2/3 * y.

your second equation is 1/2 * 3x + 2/3 * 5y = 21

you have 2 equations that need to be solved simultaneously.

they are:

3x + 5y = 36

1/2 * 3x + 2/3 * 5y = 21

multiply both sides of the second equation by 6 and leave the first equation as is to get:

3x + 5y = 36 (first equation)

9x + 20y = 126 (second equation)

multiply both sides of the first equation by 3 and leave the second equation as is to get:

9x + 15y = 108 (first equation)

9x + 20y = 126 (second equation)

subtract the first equation from the second equation to get:

5y = 18

solve for y to get y = 18/5.

replace y with 18/5 in the first original equation to get:

3x + 5y = 36 becomes 3x + 5 * 18/5 = 36

simplify to get 3x + 18 = 36

subtract 18 from both sides of this equation to get 3x = 18.

solve for x to get x = 18/3 = 6

you have x = 6 and y = 18/5.

x is the cost of one meal for one adult which is equal to 6.
y is the cost of one meal for one child which is equal to 18/5.

when the family earns 36 per week, the first equation applies and you get 3 * 6 + 5 * 18/5 = 36 which becomes 18 + 18 = 36 which becomes 36 = 36.

this confirms the first equation is correct when x = 6 and when y = 18/5.

when the family earns 21 per week, the second equation applies and you get 1/2 * 3 * 6 + 2/3 * 5 * 18/5 = 21 which becomes 9 + 12 = 21.

this confirms the second equation is correct when x = 6 and when y = 18/5.

the problem wants to know the cost per week of one child and one adult.

when the family is earning 36 per week, the cost per adult is 6 and the cost per child is 18/5.

when the family is earning 21 per week, the cost per adult is 3 and the cost per child is 12/5.

the decimal equivalent of 18/5 is equal to 3.6.

the decimal equivalent of 12/5 is equal to 2.4.

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