At the Lakewood Ice Cream Parlor, one group of friends ordered 3 small servings of ice cream and 3 large servings of ice cream for $24. Another group of friends ordered 2 small servings of ice cream and 4 large servings of ice cream for $28. How much does the ice cream cost?
The ice cream costs $
for a small serving and $
for a large serving.
3 s + 3 b = 24
2 s+ 4 b = 28
multiply first by 4 and second by 3
12 s + 12 b = 96
6 s + 12 b = 84
------------------------ subtract
6 s = 12
s = 2
Your turn
cost of small --- x
cost of large ---- y
3x + 3y = 24 ----> x + y = 8
2x + 4y = 28 ----> x + 2y = 14
subtract them:
y = 6
sub into x+y = 8 mentally to get x = 2
so one small and 1 large is $8
s+l = 8
s+2l = 14
subtract and you get large = 6
so small = 2
check:
3*2+3*6 = 24 ✅
2*2 + 4*6 = 28 ✅
ROTFL !!!!
To find the cost of the ice cream, we need to assign variables to represent the cost of a small serving and the cost of a large serving. Let's use "x" to represent the cost of a small serving and "y" for the cost of a large serving.
From the given information, we can create two equations:
Equation 1: 3x + 3y = 24 (representing the first group's order)
Equation 2: 2x + 4y = 28 (representing the second group's order)
We now have a system of two equations. We can solve this system to find the values of x and y, which represent the cost of a small serving and a large serving, respectively.
Method 1: Substitution
We can solve this system using the substitution method. Let's solve Equation 1 for x:
3x + 3y = 24
3x = 24 - 3y
x = (24 - 3y) / 3
x = 8 - y
Now substitute this expression for x in Equation 2:
2(8 - y) + 4y = 28
16 - 2y + 4y = 28
2y = 28 - 16
2y = 12
y = 12 / 2
y = 6
Substitute this value of y back into Equation 1 to find x:
3x + 3(6) = 24
3x + 18 = 24
3x = 24 - 18
3x = 6
x = 6 / 3
x = 2
So, the cost of a small serving is $2, and the cost of a large serving is $6.
The ice cream costs $2 for a small serving and $6 for a large serving.