Question

Jean Valjean is buying candlesticks and plates for his new French restaurant. He has $60 to spend on plates and candlesticks. Each plate costs $3. Each candlestick costs $6 (it comes with free candles!). Jean needs to buy a total of 15 items. How many plates and how many candlesticks does he buy? Enter the answer as an ordered pair (number of plates, number of candlesticks)

Answer 1

(10, 5)

Explanation:

Total money to spend = $60

Cost of each plate = $3

Cost of each candlestick = $6

Let number of plates bought =
`x`

Let number of candlesticks bought =
`y`

Total number of items to be bought = 15

Therefore, the first equation can be written as:

`x+y = 15` ..... (1)

Total money spent on plates = Number of plates bought
`*` Cost of each plate = $3
`x`

Total money spent on candlesticks = Number of candlesticks bought
`*` Cost of each candlestick = $6
`y`

Second equation can be written as:

`3x+6y = 60`

Dividing both sides with 3:

`x+2y=20` ..... (2)

Subtracting (1) from (2):

`y = 5`

From equation (1) :

`x = 15-5\\\Rightarrow x = 10`

Number of plates bought = 10

Number of candlesticks bought = 5

Answer as ordered pair is: (10, 5)