Jamie and Bryce each have a bag of candy containing 40 gumballs that are either red or blue. The ratio of red to blue gumballs in Jamie's bag of candy is 1:3, and the ratio of red to blue gumballs in Bryce's bag of candy is 1:4.

How many more red gumballs does Jamie have than Bryce?

Out of 40 gum balls in Jamie's bag, 10 will be red and 30 will be blue. Out of Bryce's bag, 8 will be red and 32 will be blue.

You calculate.

To solve this problem, we need to determine the number of red and blue gumballs in each person's bag and then compare the difference in the number of red gumballs.

Let's start by calculating the number of red and blue gumballs in Jamie's bag. The ratio of red to blue gumballs in Jamie's bag is 1:3. This means that for every unit of red gumballs, there are 3 units of blue gumballs.

Let's assume that the number of red gumballs in Jamie's bag is x. This means that the number of blue gumballs will be 3x, since the ratio is 1:3.

Now, let's move on to Bryce's bag. The ratio of red to blue gumballs in Bryce's bag is 1:4, which means that for every unit of red gumballs, there are 4 units of blue gumballs.

Let's assume that the number of red gumballs in Bryce's bag is y. This means that the number of blue gumballs will be 4y, since the ratio is 1:4.

Since both Jamie and Bryce have 40 gumballs in their bags, we can set up the following equation:

x + 3x = 40 (for Jamie's bag)
y + 4y = 40 (for Bryce's bag)

Simplifying these equations, we get:
4x = 40
5y = 40

Solving for x and y, we find that:
x = 10 (Jamie's red gumballs)
y = 8 (Bryce's red gumballs)

To find the difference in the number of red gumballs, we subtract the number of red gumballs in Bryce's bag from the number of red gumballs in Jamie's bag:

Difference = Jamie's red gumballs - Bryce's red gumballs = 10 - 8 = 2

Therefore, Jamie has 2 more red gumballs than Bryce.