A basket holds no more than 50 pounds of material. Each gold coin weighs about 0.5 ounces and each silver coin weighs about 0.25 ounces.You want to know the different numbers of each type of coin that could be in the basket. Write an inequality that models the weight in the basket.
Answer: 0.5g + 0.25s less than or equal to 800
Please explain how this is the answer. I'm confused.
You did a good job. What's your confusion?
Please explain
To find an inequality that models the weight in the basket, we can start by determining the weight of each type of coin in terms of pounds.
Given that each gold coin weighs about 0.5 ounces and there are 16 ounces in a pound, we can convert the weight of a gold coin to pounds by dividing by 16:
0.5 ounces ÷ 16 = 0.03125 pounds (approximately)
Similarly, each silver coin weighs about 0.25 ounces, so we can convert the weight of a silver coin to pounds:
0.25 ounces ÷ 16 = 0.015625 pounds (approximately)
Now we can create an inequality using the weights of the gold and silver coins. Let's say there are 'g' gold coins and 's' silver coins in the basket.
The weight of the gold coins, in pounds, would be 0.03125 pounds multiplied by the number of gold coins, which is 'g'. So the weight of the gold coins would be 0.03125g pounds.
Similarly, the weight of the silver coins, in pounds, would be 0.015625 pounds multiplied by the number of silver coins, which is 's'. So the weight of the silver coins would be 0.015625s pounds.
We need to find a combination of 'g' gold coins and 's' silver coins that satisfies the condition that the total weight in the basket is no more than 50 pounds. Therefore, we can write the inequality as follows:
0.03125g + 0.015625s ≤ 50
This inequality represents the weight constraint on the basket, where the weight of the gold coins multiplied by their quantity ('g') plus the weight of the silver coins multiplied by their quantity ('s') must be less than or equal to 50 pounds.