The admission to a local fair is $10 for an adult and $6 for a child. Each ride costs $1.50 for and adult and $1 for a child. Write an expression that represents how much more an adult will spend.
Let's represent the number of adults as 'a' and the number of children as 'c'.
The total cost for adults can be calculated as 10a (since each adult admission is $10 and there are 'a' adults).
The total cost for children can be calculated as 6c (since each child admission is $6 and there are 'c' children).
The cost of rides for adults can be calculated as 1.50a (since each adult ride costs $1.50 and there are 'a' adults).
The cost of rides for children can be calculated as 1c (since each child ride costs $1 and there are 'c' children).
To find out how much more an adult will spend, we need to subtract the total cost for children (admission and rides) from the total cost for adults (admission and rides).
Expression: (10a + 1.50a) - (6c + 1c)
To write an expression that represents how much more an adult will spend, we need to find the difference between the total cost for an adult and the total cost for a child.
Let's break down the costs for each item:
1. Admission:
The admission for an adult is $10.
The admission for a child is $6.
2. Rides:
Each ride costs $1.50 for an adult.
Each ride costs $1 for a child.
To find the total cost for an adult, we need to multiply the number of rides by the cost per ride and add it to the admission cost. Similarly, we do the same for a child.
Let's assume the number of rides is represented by the variable 'x'.
For an adult:
Total cost = Admission + (Cost per ride * Number of rides)
= $10 + ($1.50 * x)
= $10 + $1.50x
For a child:
Total cost = Admission + (Cost per ride * Number of rides)
= $6 + ($1 * x)
= $6 + $1x
= $6 + x
To find how much more an adult will spend, we subtract the total cost for a child from the total cost for an adult:
Expression = Total cost for an adult - Total cost for a child
= ($10 + $1.50x) - ($6 + $1x)
= $10 + $1.50x - $6 - $1x
= $4 + $0.50x
= $4.50x + $4
Therefore, the expression that represents how much more an adult will spend is $4.50x + $4.