Question

Lily sold 18 items at the street fair. She sold bracelets for $6 each and necklaces for $5 each for a total of $101. Which system of equations can be used to find b, the number of bracelets she sold, and n, the number of necklaces she sold?

Answer 1

Hello @haverstick9 ! Welcome

Your question wants us to basically translate the given information into equations.
Here is how we can think about this

"Lily sold 18 items at the street fair"
This means that (number of necklaces) + (number of bracelets) = 18
We can then replace "number of necklaces" with "n", and "number of bracelets" with "b".
This would give us one of the equations that they want.

"She sold bracelets for $6 each"
To figure out how we represent this information, we can think of the money she's making each time she sells a bracelet. If she sells one bracelet for $6 each, she gets $6. If she sells two bracelets, she gets 6+6=12 dollars. If she sells three bracelets, 6+6+6=18 dollars. And so on.
We can notice a patter in the numbers. 1 bracelet = 6, 2 bracelets = 12, 3 = 18, ...
This is just multiplying.
So, to represent "She sold bracelets for $6 each" in a math form, this would be 6 * (number of bracelets).
and we can replace "number of bracelets" with "b" just like the previous part.

Similarly,
"necklaces for $5" can be written the same way, by multiplying.
5 * (number of necklaces)

"for a total of $101"
This means that we take the two pieces of information that we just got, and add them together to get 101 dollars.
6 * (number of bracelets) + 5 * (number of necklaces) = 101


If you need any more help with this question, feel free to come back and ask.
Good luck!