I need help on this plz !

Question

Beth made wristbands and belts for a craft sale. She sold 30 of these items. Each wrist band sold for 5.50. each belt sold for 8.75. If Beth made $204 at the sale how many wristbands did she sell? How many belts did he sell. Write and solve a system of equation.

Answer 1

Navid, the first step here is to make a system of equations. This means 2 equations with the same unknown variables. Let's use x and y. 

 

We'll use x for the number of wrist bands sold and y for the number of belts sold. (Hint: These letters are completely arbitrary. You can use whatever letters you want!) 

 

Since we know Beth sold 30 items total, we can say that the number of wrist bands she sold plus the number of belts she sold has to add up to 30. So: 

 

x + y = 30

 

We've made our first equation!

 

Our next equation will deal with the money. Again, use the information you're given. How much did Beth make? $204. Ok, that's what everything has to add up to. Now, for every wrist band she sells she gets $5.50, so if she sells 2 she gets $5.50 + $5.50. If she sells 3 wrist bands, she gets $5.50 + $5.50 + $5.50 and so on. As you can see, we can multiply the number of wrist bands she's sold by their price, $5.50, to get the total amount of money Beth's earned from selling wrist bands. We can do the same thing for the belts (remembering that the money she's made from wrist bands plus the money she's made from belts has to total $204) and here's our second equation:

 

5.50x + 8.75y = 204

 

Now we need to solve this system of equations. How can we do this? Since we need to solve for both x and y, it doesn't matter which we get alone first. Let's choose x. I'm also going to start with the simpler equation, and plug back into the more complicated equation, but you could do it either way.

 

x + y = 30

     -y     -y

x= 30 - y

 

Ok. So we've solved for x. No we can plug this into our 2nd equation anywhere we see an x.

 

5.50x + 8.75y = 204

5.50(30 - y) + 8.75y = 204                                        Simplify and solve for y.

165 - 5.50y + 8.75y = 204

165 + 3.25y = 204

-165                -165

3.25y = 39

/3.25    /3.25

y = 12                                

 

Congratulations! You've solved for one variable! Now we need to go back and plug this in to the equation we made when we solved for x. (You could use any of the equations we've made, but this is going to be the simplest one.)

 

x = 30 - y

x = 30 - (12)

x = 18

 

Now the only thing to check is that you keep straight which variable you assigned to which item so that you can be sure you write your answer correctly. Since x stood for the number of wrist bands sold and y was the number of belts sold, we can write our answer: Beth sold 18 wrist bands and 12 belts at the craft sale. 

 

Answer 2

let's make w stand for wristbands and b for belts.

Now let's list what we know:

w + b = 30

(the total number of items sold is 30)

5.5w + 8.75b = 204

(the amount of money made is the total of the selling point number and selling point of each item put together)

 

I would not suggest using elimination for this. A whole lot of fractions can make this messy. Let's try substitution in this case:

w + b = 30 let's isolate w:

w = 30 - b

Now we use that value of w and put that into our equation so that we can solve for b:

5.5(30 - b) + 8.75b = 204

165 - 5.5b + 8.75b = 204

- 5.5b + 8.75b = 39

3.25b = 39

Divide both sides by 3.25:

b = 12

 

So Beth sold 12 belts.

w = 30 - 12

w = 18

And she sold 18 wristbands.

 

Now let's check our answer:

5.5 * 18 + 8.75 * 12 = 204

99 + 105 = 204

204 = 204