If A is directly proportional to C and B is directly proportional to C, prove that each of the following is directly proportiona
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Answer:
Step-by-step explanation:
Let's make a system of equations.
First, define the variables.
Let s= small cups and g= large cups
Next, make 2 equations. 1 for the money and 1 for the number of cups.
<u>Money</u>
- A small cup costs 1.25 and a large cup costs 2.50. The total money made is 265.
- 1.25s+2.50g=265
<u>Number</u>
- A total of 155 cups of lemonade were sold. The sum of small cups and large cups sold will equal 155.
- s+g=155
Here is our system of equations:
Now, solve. Let's isolate a variable in the 2nd equation, so we can plug it in after.
- Subtract g from both sides of the equation.
- s+g=155
- s+g-g=155-g
- s=155-g
Now we know that s is equal to 155-g. We can substitute (155-g) in for s in the first equation.
Distribute the 1.25
- 1.25(155-g)= (1.25*155)+ (1.25*-g)= 193.75-1.25g
Work to isolate the variable. Subtract 193.75 from both sides of the equation and combine like terms on the left.
(Subtract 193.75)
(Combine like terms).
1.25 and g are being multiplied. The inverse of multiplication is division. Divide both sides by 1.25
Now we know that 57 large cups were sold. Plug 57 back into the original second equation to find the small cups.
Subtract 57 from both sides of the equation to isolate the variable, s.
Ashley sold 57 large cups and 98 small cups.