Jane purchases 20 candles for her family members. Tall candles cost $6 each and short candles cost $4 each. She spends a total of $100.

Question

Part A: Jane is buying X tall candles and Y short candles. Which system of equations can be used to find the value of x and y.

Part B; how many tall candles did Jane buy/?

Answer 1

Since "x" and "y" represent quantities, this means that these amounts added together would be the total number of candles purchased - in this case 20

So the resulting equation would be

x+y= 20

Next we are told cost of each and total amount spent. Keep "dollars" with "dollars", meaning that cost per candle on one side of the equation should be with total cost on other side of equation.

6x + 4y = 100

To solve you will either solve by substitution or elimination. Substitution means that you will solve the first equation for either x or y and then substitute into the second equation:

x + y = 20

Solve for y by subtracting x from both sides

y = 20 - x

Substitute "20 - x" into second equation for "y"

6x + 4(20-x) = 100

Distribute

6x + 80 - 4x = 100

Combine like terms

2x + 80 = 100

Subtract 80 from both sides

2x = 20

Divide both sides by 2

x = 10

Since she purchased a total of 20 candles, she bought 10 tall candles and 10 short candles