On a hot summer day, Sunny bought 18 ice creams for her team members. Some were $7 each, and the others were $10 each. If she paid $165 in total, how many $7 ice creams did she buy?
number of cheaper ice creams --- x
number of more expensive ones ---- 18-x
solve for x
7x + 10(18-x) = 165
( I know things are getting expensive, but $10 ice creams ???)
To solve this problem, we can set up a system of equations. Let's say Sunny bought x ice creams for $7 each, and y ice creams for $10 each.
The first equation represents the total number of ice creams: x + y = 18.
The second equation represents the total cost: 7x + 10y = 165.
To find the number of $7 ice creams, we need to solve this system of equations.
We can apply the substitution method to solve the system:
1. Solve the first equation for x: x = 18 - y.
2. Substitute the value of x in the second equation: 7(18 - y) + 10y = 165.
3. Distribute and simplify: 126 - 7y + 10y = 165.
4. Combine like terms: 3y = 39.
5. Divide both sides by 3: y = 13.
Therefore, Sunny bought 13 ice creams for $10 each.
Now, substitute the value of y back into the first equation to find the number of $7 ice creams:
x + 13 = 18
x = 18 - 13
x = 5
Sunny bought 5 ice creams for $7 each.
So, she bought 5 $7 ice creams.