Question

Greg went to Bed Bath and Beyond to buy Christmas gifts for his family this year. In his first trip he bought 4 candles, 5 wallflowers, and 6 lotions for a total of $123. Greg forgot some people on his list the first time so he makes a second trip and spent $48 to buy 2 candles, 3 wallflowers, and 1 lotion. The price of a lotion is 2 less than 2 times the price of a wallflower. How much does each item cost?

Answer 1

Price of Candle: 12.5

Price Wallflower: 5

Price of Lotion: 8

Explanation:

Let cost of a candle =
`x`

Let cost of a wallflower =
`y`

Let cost of a lotion =
`z`

Cost of 4 candles = 4
`x`

Cost of 5 wallflowers = 5
`y`

Cost of 6 lotions = 6
`z`

Cost of 2 candles = 2
`x`

Cost of 3 wallflowers = 3
`y`

Cost of 1 lotion =
`z`

As per question statement:

`4x+5y+6z=123 .... (1)\\2x+3y+z=48 ...... (2)\\z=2y-2 ..... (3)`

Using equation (3) in (1) and (2), the equations get reduced to :

`\Rightarrow 4x+17y = 135 ..... (4)\\\Rightarrow 2x+5y = 50 ..... (5)`

Multiplying (5) with 2 and subtracting from equation (1):

`7y = 35\\\Rightarrow y = 5`

By equation (3):

`\Rightarrow z =8`

By equation (4):

`\Rightarrow x = 12.5`

Therefore, the answer is:

Price of Candle: 12.5

Price Wallflower: 5

Price of Lotion: 8