## 1. Jin bought 3 small candles and 1 medium candle for \$3.85. Trish bought 4 small candles and 5 medium candles for \$10.45. (a) W

Question

1. Jin bought 3 small candles and 1 medium candle for \$3.85. Trish bought 4 small candles and 5 medium candles for \$10.45.

(a) Write a system of equations that you could use to find the cost of each size of candle. Use s for the cost of a small candle and m for the cost of a medium candle.

(b) Solve the system using either linear combination or substitution.

(c) Mark bought 2 small candles and 1 medium candle. How much did he pay in all?

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1. We will use s for the cost of a small candle and m for the cost of a medium candle.

(a)
The candles and price for Jin can be written as:
3s+1m=\$3.85
The candles and price for Trish can be written as:
4s+5m=\$10.45

The system of equations that we have is:
3s+1m=\$3.85
4s+5m=\$10.45

(b)
We will use substitution to solve this problem.
From the first equation we can find out m:
3s+1m=\$3.85
1m=\$3.85-3s

Now we insert this into second equation and we solve it for s:
4s+5(\$3.85-3s)=\$10.45
4s+\$19.25-15s=\$10.45
-11s=-8.8
s=\$0.8
Now we can find m:
m=\$3.85-3*\$0.8
m=\$3.85-\$2.4
m=\$1.45

(c)
The candles and price for Jin can be written as:
2s+1m=price
We can insert values for s and m:
2*\$0.8+\$1.45=price
price=\$1.6+\$1.45
price=\$3.05