Why did Populist Party want to have a monetary system based on both silver and gold?

Please note that I revised your question to make it accurate. The Populist Party wanted to have a monetary system based on both silver and gold. They wanted a bi-metallic money system. The Republican Party wanted a monetary system based only on gold.
The Populist Party represented farmers. Farmers were suffering tremendously. The prices for their crops were very low. They also had to pay extremely high interest rates on the loans they received. If they couldn’t pay back their loans, they would lose their farm. One way to increase prices and bring interest rates down was to increase the money supply. When there is more money in the economy, prices tend to rise since people have more money to spend. This might help the farmers get higher prices for their crops. Additionally, if there is more money available, banks will have more money to loan to people. Since the money supply isn’t as tight, meaning more money is available for loans, the interest rates on the loans should drop.
Another advantage of having a larger money supply is that those people who are in debt will be repaying their loans with dollars that won’t buy as much as before because the increase in the money supply will lead to inflation. Thus, the purchasing power of the dollar will drop, which means that the farmers would be repaying their loans with dollars that wouldn’t buy as much as in the past.