A group of friends are ordering food. The total amount that they can spend on their food bill is $[tex]$41$[/tex], including the delivery charge of $[tex]$6$[/tex]. The equation below represents the situation, where [tex]$x$[/tex] is the cost of each friend's meal.
[tex]$6+a x=41$[/tex]
The cost of each friend's meal in terms of [tex]$a$[/tex] is [ ]
The cost of each friend's meal when the number of friends is 5 is $[tex]$[$/tex] [ ].
Answer (1)
First, isolate the term with x by subtracting 6 from both sides of the equation: a x = 35 .
Then, solve for x by dividing both sides by a : x = a 35 .
Substitute a = 5 into the equation to find the cost when there are 5 friends: x = 5 35 .
Finally, simplify to find the cost per friend: x = 7 , so the cost is 7 .
Explanation
Understanding the Problem We are given the equation 6 + a x = 41 , where x is the cost of each friend's meal and a is the number of friends. We need to find the cost of each friend's meal in terms of a , and then find the cost when a = 5 .
Isolating the Term with x First, let's solve the equation for x in terms of a . We start with the equation: 6 + a x = 41
Simplifying the Equation Subtract 6 from both sides of the equation: a x = 41 − 6
a x = 35
Finding x in terms of a Now, divide both sides by a to solve for x :
x = a 35 So, the cost of each friend's meal in terms of a is a 35 .
Substituting a = 5 Next, we need to find the cost of each friend's meal when the number of friends is 5, which means a = 5 . Substitute a = 5 into the expression for x :
x = 5 35
Calculating the Cost Now, simplify the fraction: x = 7 So, the cost of each friend's meal when there are 5 friends is $7 .
Examples
Imagine you're organizing a pizza party with your friends. You have a total budget, including delivery fees, and you want to figure out how much each person can spend on their pizza slice. This problem helps you calculate the individual cost based on the number of friends and the total budget. Understanding how to solve such equations can help you manage budgets, split costs fairly, and plan events effectively, ensuring everyone enjoys the party without overspending.
