Question

You are making gift baskets. each basket will contain three different types of candles: tapers, pillars ad jar candles. tapers cost $1 each, pillars cost $4 each, and jar candles cost $6 each. you put 8 candles costing a total of $24 in each basket, and you include as many tapers as pillars and jar candles combined. how many of each type of candle will be in a basket?

Answer 1

Let
x = the number of tapers (each coss $1)
y = the number of pillars (each costs $4)
z = the number of jars (each costs $6)

There are 8 candles in each basket, therefore
x + y + z = 8                   (1)

The cost per basket is $24, therefore
x + 4y + 6z = 24             (2)

The number of tapers equals the sum of pillars and jars, therefore
x = y + z                          (3)

Substitute (3) into (1) and into (2).
y + z + y + z = 8
2y + 2z = 8
y + z = 4                           (4)

y + z + 4y + 6z = 24
5y + 7z = 24                     (5)
From (4), y = 4 -z. Substitute into (5).
5(4 - z) + 7z = 24
2z + 20 = 24
2z = 4
z = 2
y = 4 - z = 4 - 2 = 2
x = y + z = 2 + 2 = 4

Answer: 4 tapers, 2 pillars, 2 jars.