Final answer:
By setting up a system of equations and solving for the variables, we find that 4 boy gifts and 7 girl gifts were purchased for the total of $18 with 11 friends attending the party.
Step-by-step explanation:
To determine how many boy gifts and girl gifts were purchased, we can set up a system of equations based on the given information. Let's let x represent the number of boy gifts and y represent the number of girl gifts. The cost of boy gifts is $1 each, and the cost of girl gifts is $2 each. Given that the total amount spent on gifts is $18 and there were 11 friends, we can write the following two equations:
- Equation for cost: x + 2y = 18 (Total cost equation)
- Equation for the number of gifts: x + y = 11 (Total gifts equation)
To solve this system, we can use the second equation to express x in terms of y: x = 11 - y. We can then substitute this expression for x into the first equation: (11 - y) + 2y = 18. Simplifying this equation gives us y = 7, which means there were 7 girl gifts. To find the number of boy gifts, we substitute y = 7 into the equation x + y = 11, giving us x = 4. Therefore, 4 boy gifts and 7 girl gifts were purchased.