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.

Answer 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