How do you write equations and then solve using substitution?

number sold to boys = b
number sold to girls = g
We are given that b + g = 62    .....equation 1
We are also told that
$5*b + $4*g = $289   i.e.
5b + 4g = 289   .....equation 2
multiply equation 1 by 4
4b + 4g = 248   subtract from equation 2
b = 41  Answer
substituute for b in equation 1
41 + g = 62
g = 21  Answer
check in equation 1
21 + 41 = 62  correct
check in equation 2
41*5 + 21*4 = 289 correct.

So, from this, you have two equations.
The number of people he sold it to is equal to 62, and is basically the sum of girls and boys put together.

g+b=62 (where "b" is the number of boys and "g" is the number of girls)

Then, from that, you can say that, if each girl bought a pocket protector for $4, then the total amount that they spent is equal to 4*g, or 4 dollars per girl. The same is dome for boys at 5*b, and you know the grand total is 289. So,

4*g + 5*b = 289

Now, just substitute.

g + b = 62; g = 62 - b
4*g + 5*b = 4*(62 - b) + 5*b = 248 - 4*b + 5*b = 248 + b = 289; b = 289 - 248 = 41

So the number of boys is 41. As g + b = 62, g = 21.

And that's that.

Let the number of the product sell to girls be "x" and to boys be "y"

1) The question suggested that he sells the product to girls for 4$, so, the amount of money he received must be 4x. Similarly, if he sells to boys for 5$, the amount of money from boys must be 5y. The question suggested that the money he made from this sales be $289, so both money from girls and boys must be combined to get $289, that is to say in equation, 4x+5y=289

2) The question noted he sold it for 62 pieces, therefore from the variable we set above, x+y=62

You will get two equations. 4x+5y = 289 and x+y=62

As you can rewrite x+y=62 as y=62-x, use the value of y=62-x to substitute "y" in 4x+5y = 289. (We choose to substitute "y" with "x cause we would like to find the amount of product sell to girls. Refer to the above variable, it is "x") then try to solve the equation. If you do it correctly, you will get y=41 and x=21. Therefore the amount that Billy sold to girls is 21 protectors. Good luck on solving!

Let the number of Boys be B and the number of Girls be G

The equation would be ($4 x G) + ($5 x B) = $289

At this point we only know that 62 were sold. You are unable to say how many were sold to Girls without trial and error.

The quickest way would be to split the number sold between Boys and Girls equally - so 31 to Boys and 31 to girls.

Substitute these in the equation above and you get

($4 x 31) + ($5 x 31) or  $124 + $155 = $279

This is $10 less than the $289 we were told that all 62 were sold for.

So it stands to reason that 10 more were sold to Boys than were to Girls to make up the $10 shortfall. (As boys pay $1 more)

So you know 41 were sold to Boys and only 21 were to Girls.

This can be proven by substituting 41 and 21 into the equation.

($4 x 21) + ($5 x 41) or   $84 + $205 = $289

Hope that helps