Question 1054997
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.