Question

A busload of campers stopped at a dairy stand for ice cream. They ordered 84 cones, some soft-serve at

$1.50 each and the rest hard-pack at $1.25 each. If the total bill was $113.00, how many of each type of
cone were ordered?
soft-serve cones were ordered

Answer 1

The total number of cones was 84. So s (number of soft-serve) + h (number of hard-pack) = 84.
The total bill was 113.00. To get the equation, first you have to put the individual types as variables. “1.50s” means the price of soft serve x number of soft serve. “1.25h” means the price of hard pack x number of hard pack. Then make the full equation: 1.50s + 1.25h = 113.00.
So now you have a system of equations. Now you have to find one variable and use it to figure out the other. Since we know s + h = 84, just s = 84-h.
Now we could plug that instead of the s in the second equation to get 1.50 (84-h) + 1.25h = 113.00. By distributing, we get that (126-1.50h) + 1.25h = 113.00. Then combine like terms to get 126 - .25h = 113.00. Then get h by itself by subtracting 126 from both sides and then dividing both sides by -.25 to get h = 52.
Now that we know h, we can plug it in instead of the s variable to get 84-52=32.
That means 32 soft serve and 52 hard pack were ordered.