Sierra starts with 260 cans of food for a food drive. She collects 8 more cans every day. Brian starts with 650 cans of food for a food drive. He collects 5 more cans every day. What is x, the number of days that need to pass in order for Sierra and Brian to have the same number of cans of food?
Set up an equation first:
260 + 8x = 650 + 5x
Now solve for x:
3x = 390
Divide both sides by 3:
x = 130
So 130 days need to pass for Sierra and Brian to have the same number of cans of food.
Let's assume that after x days, Sierra and Brian will have the same number of cans of food.
After x days, Sierra will have 260 + 8x cans of food.
After x days, Brian will have 650 + 5x cans of food.
To find the value of x, we need to solve the equation:
260 + 8x = 650 + 5x
Subtracting 260 from both sides gives:
8x = 390 + 5x
Subtracting 5x from both sides gives:
3x = 390
Dividing both sides by 3 gives:
x = 130
Therefore, it will take 130 days for Sierra and Brian to have the same number of cans of food.
To solve this problem, we can set up an equation to represent the number of cans collected by each person over time.
For Sierra:
Number of cans collected by Sierra = 260 + 8x, where x is the number of days that have passed.
For Brian:
Number of cans collected by Brian = 650 + 5x, where x is the number of days that have passed.
Since we want to find the number of days when both Sierra and Brian have the same number of cans, we can set the equations equal to each other and solve for x:
260 + 8x = 650 + 5x
First, subtract 5x from both sides to isolate the x term:
260 + 3x = 650
Next, subtract 260 from both sides to isolate the constant term:
3x = 390
Finally, divide both sides by 3 to solve for x:
x = 130
Therefore, it would take 130 days for Sierra and Brian to have the same number of cans of food.