The equation below shows how Mandy decides how much juice to buy for a party. In the equation, g is the number of gallons of juice she buys, and t is the length of the party in hours.
g= 3t + 5
What is + 5?
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To determine how much juice Mandy should buy for a party, you can follow these steps using the given equation:
Step 1: Determine the length of the party in hours.
Example: Let's say the party will last for 4 hours. Therefore, t = 4.
Step 2: Substitute the value of t into the equation.
In this case, replace t with 4 in the equation:
g = 3(4) + 5.
Step 3: Simplify the equation.
Multiply 3 by 4: 3(4) = 12.
So the equation becomes: g = 12 + 5.
Step 4: Perform the addition in the equation.
12 + 5 = 17.
Therefore, Mandy should buy 17 gallons of juice for a 4-hour party, according to the given equation.
To understand how Mandy decides how much juice to buy for a party using the equation g = 3t + 5, we need to break down the equation.
The equation g = 3t + 5 represents a linear relationship between the number of gallons of juice, g, and the length of the party in hours, t.
In this equation, the coefficient 3 represents the rate at which the number of gallons of juice increases with the length of the party. So, for every hour the party lasts, Mandy buys 3 more gallons of juice.
The constant term 5 represents the initial amount of juice Mandy buys, regardless of the party length. It is the y-intercept, which is the value of g when t is 0. In this case, Mandy buys 5 gallons of juice even if the party is not happening.
To find out how much juice Mandy will buy for a specific party length, plug in the value of t into the equation and solve for g.
For example, if the party length is 2 hours, we can substitute t = 2 into the equation:
g = 3(2) + 5
g = 6 + 5
g = 11
So, for a 2-hour party, Mandy will buy 11 gallons of juice.