Question

A candle shop sells scented candles for $16 each and unscented candles for $10 each.The shop sells 28 candles today and makes $400.Write a system of
linear equations that represents the situation

Answer 1

Let the number of scented candles be represented with   s.

Let the number of unscented candles be represented with   u.

The total number sold were 28.

s + u = 28.

Total cost made was $400, from selling both scented and unscented.

Since each scented cost $16 and unscented cost $10

16s + 10u = 400

Hence:

System of linear equations:

    s  +  u  = 28

16s + 10u = 400

Answer 2

Lets call s the number of scented candles sold, and u the number of unscented candles sold and write as an equation the info provided in the problem:
16s + 10u = 400
s + u = 28
that is, the first equation synthesize the fact that the amount of unscented candles times its quantity plus the amount of scented candles times its quantity equals $400
and the second equation synthesize the fact that the number of scented and unscented candles add up to 28
Now you just need to solve the system of two linear equations with two unknowns to get the specific value of the scented and unscented candles.