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 $41, including the delivery charge of $6. The equation below represents the situation, where $x$ 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 $\boxed{}$ .
The cost of each friend's meal when the number of friends is 5 is $\boxed{}$.
Answer (2)
Solve the equation 6 + a x = 41 for x to express the cost of each meal in terms of a : x = a 35 .
Substitute a = 5 into the equation x = a 35 .
Calculate the cost of each meal when a = 5 : x = 5 35 = 7 .
The cost of each friend's meal when the number of friends is 5 is 7 .
Explanation
Problem Analysis Let's analyze the problem. We are given the equation 6 + a x = 41 , where x represents the cost of each friend's meal and a represents 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 .
Solving for x in terms of a First, we solve the equation 6 + a x = 41 for x in terms of a .
Subtract 6 from both sides of the equation: a x = 41 − 6 a x = 35 Divide both sides by a :
x = a 35
Finding the cost when a=5 Now, we find the cost of each friend's meal when the number of friends is 5, i.e., when a = 5 .
Substitute a = 5 into the expression x = a 35 :
x = 5 35 x = 7
Final Answer Therefore, the cost of each friend's meal in terms of a is a 35 , and the cost of each friend's meal when the number of friends is 5 is $7 .
Examples
Understanding how to split costs and account for fixed charges is a common scenario. For example, imagine you and your friends are planning a road trip. The total budget is limited, and there are fixed costs like gas and car rental. By using a similar equation, you can determine how much each person can spend on food and activities, ensuring you stay within budget while accounting for the shared expenses.
The cost of each friend's meal in terms of a is a 35 and the cost when there are 5 friends is $7.
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