Can someone help me with this problem I really don’t know how to work it out and I’m getting frustrated please help..
1 answer:
Answer:
1 cake and 6 pies
Step-by-step explanation:
Let c represent the number of cakes Alice and George can make. Likewise, let p represent the number of pies.
Then the amount of flour they need (in cups) is ...
3c + 2p . . . . cups of flour needed
And the amount of sugar needed is ...
2c + 1.5p . . . cups of sugar needed
__
They want to use all 15 cups of flour they have, and all 11 cups of sugar, so the amounts above need to match the amounts on hand:
3c + 2p = 15
2c + 1.5p = 11
We can solve these equations various ways. One of my favorite is to use a graphing calculator. (See attached) It tells us that Alice and George can make 1 cake and 6 pies with the flour and sugar they have.
_____
If you want to solve these equations algebraically, there are several methods for that, too. Here, we can multiply the first one by 2/3 and subtract the result from the second one:
(2c +1.5p) -(2/3)(3c +2p) = (11) -(2/3)(15)
2c +3/2p -2c -4/3p = 11 -10 . . . . . eliminate parentheses
1/6p = 1 . . . . . . . . . . . . . . . . . . . . . .collect terms
p = 6 . . . . . . . . . . . . . . . . . . . . . . . . multiply by 6
Substituting into the first equation gives ...
3c +2·6 = 15 . . . substitute 6 for p
3c = 3 . . . . . . . . subtract 12
c = 1 . . . . . . . . . . divide by 3
These values tell us Alice and George can make 1 cake and 6 pies with the flour and sugar they have.
You might be interested in
Hi there! The answer is 72 guests.
To find our answer we need to set up and solve an equation. Let the total number of guests be represented by g. The cost per guest is $13.50
Therefore the cost for all of the guests will be $13.50 × g.
To find the total cost we need to add the additional fee of $540 to cover linens and tableware.
Now we've found our equation.
Subtract 540.
Divide by 13.5
Therefore, there are 72 guests. The answer is 72.
~ Hope this helps you!
To find our answer we need to set up and solve an equation. Let the total number of guests be represented by g. The cost per guest is $13.50
Therefore the cost for all of the guests will be $13.50 × g.
To find the total cost we need to add the additional fee of $540 to cover linens and tableware.
Now we've found our equation.
Subtract 540.
Divide by 13.5
Therefore, there are 72 guests. The answer is 72.
~ Hope this helps you!