Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
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]$6+ax=41$[/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 (2)
Express the cost of each meal, x , in terms of the number of friends, a , by rearranging the equation: x = a 35 .
Substitute a = 5 into the equation to find the cost per meal when there are 5 friends: x = 5 35 .
Simplify the expression to find the cost per meal: x = 7 .
The cost of each friend's meal when the number of friends is 5 is 7 .
Explanation
Understanding the Problem Let's break down this problem step by step so we can understand how to find the cost of each friend's meal. We know the total budget, the delivery charge, and the equation that relates these values.
Setting up the Equation The problem states that the total amount the group can spend is $41 , which includes a delivery charge of $6 . The equation given is:
6 + a x = 41
where x represents the cost of each friend's meal, and a represents the number of friends. Our goal is to find x in terms of a , and then find the value of x when a = 5 .
Finding the Cost in Terms of a First, let's solve the equation for x in terms of a . We start with:
6 + a x = 41
Subtract 6 from both sides:
a x = 41 − 6
a x = 35
Now, divide both sides by a to isolate x :
x = a 35
So, the cost of each friend's meal in terms of a is a 35 .
Finding the Cost When a = 5 Next, we want to find the cost of each friend's meal when there are 5 friends, so we substitute a = 5 into our expression for x :
x = 5 35
Now, simplify the fraction:
x = 7
Therefore, when there are 5 friends, each friend's meal costs $7 .
Final Answer So, the cost of each friend's meal in terms of a is a 35 , and when there are 5 friends, the cost of each meal is $7 .
Examples
Imagine you and your friends are planning a pizza night. You have a total budget, and you know there's a delivery fee. Using the equation we solved, you can quickly figure out how much each person can spend on their pizza slice to stay within budget. This kind of calculation is useful not just for pizza, but for any group outing where you need to split costs evenly while accounting for fixed expenses.
The cost of each friend's meal in terms of the number of friends is a 35 . When there are 5 friends, the cost of each meal is 7 .
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