Question

A local shelter received a generous donation of $2,346 to purchase blankets, sweaters, and coats. Blankets cost $6 each, sweaters cost $18 each, and coats cost $24 each. The number of blankets they purchase is seven times the number of coats. The number of sweaters purchased is twice the number of coats. Write a system of equations that can be used to determine the number of blankets, x, the number of sweaters, y, and the number of coats, z, purchased by the shelter.

Answer 1

To write a system of equations that can be used to determine the number of blankets (x), sweaters (y), and coats (z) purchased by the shelter, we can use the given information:

1. The number of blankets purchased is seven times the number of coats:

- This can be expressed as: x = 7z.

2. The number of sweaters purchased is twice the number of coats:

- This can be expressed as: y = 2z.

3. The total cost of the purchase is $2,346:

- The cost of blankets is $6 each, so the cost of x blankets is 6x.

- The cost of sweaters is $18 each, so the cost of y sweaters is 18y.

- The cost of coats is $24 each, so the cost of z coats is 24z.

- The total cost can be expressed as: 6x + 18y + 24z = 2346.

Therefore, the system of equations is:

- x = 7z

- y = 2z

- 6x + 18y + 24z = 2346

By solving this system of equations, we can determine the values of x, y, and z, representing the number of blankets, sweaters, and coats purchased by the shelter, respectively.

I hope this explanation helps you understand how to write a system of equations based on the given information. If you have any further questions, feel free to ask!