Question

example 2: a weightlifter uses a total of 12 plates to add 260 pounds to a bar. he uses 45 - pound plates and 10 - pound plates. write and solve a system of equations to find the number x of 45 - pound plates and the number y of 10 - pound plates he uses.

Explanation:

Step1: Define variables and set up equations

Let \( x \) be the number of 45 - pound plates and \( y \) be the number of 10 - pound plates.
We know two things: the total number of plates is 12, so \( x + y=12\).
The total weight is 260 pounds, and since each 45 - pound plate contributes 45 pounds and each 10 - pound plate contributes 10 pounds, we have \( 45x + 10y=260\).

Step2: Solve the system of equations

From the first equation \( x + y = 12\), we can express \( y\) in terms of \( x\) as \( y=12 - x\).
Substitute \( y = 12 - x\) into the second equation \( 45x+10y = 260\):
\[

$$\begin{align*} 45x+10(12 - x)&=260\\ 45x + 120-10x&=260\\ 35x&=260 - 120\\ 35x&=140\\ x&=\frac{140}{35}\\ x& = 4 \end{align*}$$

\]
Then substitute \( x = 4\) into \( y=12 - x\), we get \( y=12 - 4=8\).

Answer:

The number of 45 - pound plates \( x = 4\) and the number of 10 - pound plates \( y = 8\).