contestada

A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 5 grams and the amount of gold in each necklace is 22 grams. The jeweler made a total of 17 bracelets and necklaces using 238 grams of gold. Write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define the variables that you use to write the system.

Respuesta :

ez0225

Answer:

238 = 5x + 22y

x + y = 17

x = number of bracelets

y = number of necklaces

Step-by-step explanation:

238 (total grams of gold) = (5 grams per bracelet * x number of bracelets) + (22 grams per necklace * y number of necklaces)

(x number of bracelets) + (y number of necklaces) = 17 total pieces of jewlery

The number of bracelets made is 8  and the number of necklaces made are  9.

Concept:

  1. We will assign variables for the number of bracelets and the number of necklaces made.
  2. For the first equation, We will multiply each number by their respective weights of ornament and equate it to the total weight of gold available.
  3. For the second equation, we will add no of necklaces and bracelets and equate it with the total number of ornaments made.
  4. Finally, we will solve both equations and will find the number of bracelets and necklaces.

How to solve the given question?

  • Let the number of bracelets be "x" and the number of necklaces made be "y".
  • As there is 5gm gold in each bracelet, the total gold used in the bracelet will be 5x gms.
    And, As there is 22gm gold in each necklace, the total gold used in the necklace will be 22y gms.
  • As total 17 ornaments are made from 238gms gold, following are the given set of equations:
              x +      y =  17        ..... (1)
            5x + 22y = 238      ..... (2)
  • For solving the above two equations by elimination approach, multiplying equation (1) with 5 and subtracting it from equation (2), we get,
                  y = 9
    Substituting, y = 9 in equation (1), we get x = 8.

Thus, the number of bracelets made is 8  and the number of necklaces made is 9.

Learn more about equations here:

https://brainly.com/question/19249122

#SPJ2


Otras preguntas