Question

Judy is selling small candles at the fair for $4 each and large candles for $6 each. She collected $144 selling a total of 28 candles. How many of each candle did she sell? Use x for the small candles and y for the large candles.

small candle x= blank candles
large candle y = blank candles

Answer 1

small candles-x

large -y

144-4x=6y

28-x=y

28-y=x

(28-x)6+4x=144

168-6x+4x=114

-2x=-54

2x=54

x=27

27 small and 1 large

Answer 2

Number of small candles = 12

Number of large candles = 16

Explanation:

Total candles = 28

x + y = 28 ---------------(I)

Cost of 'x' small candles = 4 *x = 4x

Cost of 'y' large candles = 6 *y = 6y

Total amount = $144

4x + 6y = 144 -------------(II)

Multiply equation (I) by (-4) and then add the equation. So, x will be eliminated and we can find the value of 'y'

(I) * (-4) -4x - 4y = -112

(II) 4x + 6y = 144 {Now, add}

2y = 32

y = 32/2

y = 16

Plug in y = 16 in equation (I)

x + 16 = 28

x = 28 - 16

x = 12