Solve graphically

Question

You sell small and large candles at a craft fair. Small candles sell for $2 each, while large candles sell for $3 each. You collect $30 selling a total of 12 candles. How many of each type of candles did you sell? (Solve graphically)

Answer 1

Let small candles be 'x' and large candles be 'y'

Total number of candles,

x+y = 12 (Given) --------------------1

Small candle rate = $2

so, rate of 'x' candles = 2x

Large candle rate = $3

so, rate of 'y' candles = 3y

Total amount after selling 2x and 3y candles,

2x+3y =30 (Given) ------------------2

solving equations 1 and 2,

2x+3y = 30

2(x+y) = 2*12 , {make same x or y component to solve the equation}

subtracting the above two equations we get,

y = 6

substituting the above value to equation 1 gives

x = 12-6 = 6

Therefore, there are 6 small and 6 large candles.

Answer 2

x+y = 12

2x+3y = 30

2x + 3(12-x) = 30

2x + 36 - 3x = 30

36 - x = 30

x = 6

y=6

Answer 3

You sell small and large candles at a craft fair. Small candles sell for $2 each, while large candles sell for $3 each. You collect $30 selling a total of 12 candles. How many of each type of candles did you sell? (Solve graphically).

You would set up two equations for this (S for small candles, L for Large candles)

1. One equation will be the dollar amount collected (money)
2. 2(S) + 3(L) = 30
3. The other equation will be the total candles sold (quantity)
4. S + L = 12

Next you solve for one of the two variables and plug it into the opposite equation. So, if we used the second equation and solved for S = 12 - L, then plug the value of S into the first equation; we would get:

1. 2(12 - L) + 3(L) = 30 now you can solve for L (the number of Large candles)
2. 24 - 2L + 3L = 30
3. 24 + L = 30
4. L = 6
5. To solve for S, just use the 2nd equation and plug in the value for L you just got
6. S + 6 = 12
7. S = 6

So you sold 6 of each size! I hope the process of getting to the answer helped you. Do you have any questions?