Jake ate seven times more jelly beans as Sam. Together they ate 128 jelly beans. How many jelly beans did each person eat?
Let x = Sam's jelly beans.
x + 7x = 128
8x = 128
x = 16
To solve this problem, we need to set up and solve a system of equations. Let's use variables to represent the number of jelly beans Jake and Sam ate.
Let's say the number of jelly beans Sam ate is x. According to the problem, Jake ate seven times more jelly beans than Sam, so Jake ate 7x jelly beans.
We also know that together they ate 128 jelly beans, so the total number of jelly beans can be expressed as:
x (Sam's jelly beans) + 7x (Jake's jelly beans) = 128
To solve this equation, we combine like terms:
8x = 128
Next, we isolate x by dividing both sides of the equation by 8:
8x/8 = 128/8
x = 16
Therefore, Sam ate 16 jelly beans, and since Jake ate seven times more, Jake ate 7 * 16 = 112 jelly beans.
So, Sam ate 16 jelly beans, and Jake ate 112 jelly beans.