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Complete Question
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar. Let x = the number of packages of pasta and y = the number of jars of pasta sauce. One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry? Explain your reasoning.
Answer:
Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.
Step-by-step explanation:
Let
x = the number of packages of pasta
y = the number of jars of pasta sauce.
He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
x + 1.5y ≤ 20....... Equation 1
x = 20 - 1.5y
x × $1 + y × $3 = $36
x + 3y ≤ 36..... Equation 2
20 - 1.5y + 3y = 36
-1.5y + 3y = 36 - 20
1.5y = 16
y = 16/1.5
y = 8
And x = 8
Therefore,
Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.
the equilibrium point, is when Demand = Supply, namely, when the amount of "Q"uantity demanded by customers is the same as the Quantity supplied by vendors.
That occurs when both of these equations are equal to each other.
let's do away with the denominators, by multiplying both sides by the LCD of all fractions, in this case, 12.
![\bf \stackrel{\textit{Supply}}{-\cfrac{3}{4}Q+35}~~=~~\stackrel{\textit{Demand}}{\cfrac{2}{3}Q+1}\implies \stackrel{\textit{multiplying by 12}}{12\left( -\cfrac{3}{4}Q+35 \right)=12\left( \cfrac{2}{3}Q+1 \right)} \\\\\\ -9Q+420=8Q+12\implies 408=17Q\implies \cfrac{408}{17}=Q\implies \boxed{24=Q} \\\\\\ \stackrel{\textit{using the found Q in the Demand equation}}{P=\cfrac{2}{3}(24)+1}\implies P=16+1\implies \boxed{P=17} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{Equilibrium}{(24,17)}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7BSupply%7D%7D%7B-%5Ccfrac%7B3%7D%7B4%7DQ%2B35%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7BDemand%7D%7D%7B%5Ccfrac%7B2%7D%7B3%7DQ%2B1%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20by%2012%7D%7D%7B12%5Cleft%28%20-%5Ccfrac%7B3%7D%7B4%7DQ%2B35%20%5Cright%29%3D12%5Cleft%28%20%5Ccfrac%7B2%7D%7B3%7DQ%2B1%20%5Cright%29%7D%20%5C%5C%5C%5C%5C%5C%20-9Q%2B420%3D8Q%2B12%5Cimplies%20408%3D17Q%5Cimplies%20%5Ccfrac%7B408%7D%7B17%7D%3DQ%5Cimplies%20%5Cboxed%7B24%3DQ%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20found%20Q%20in%20the%20Demand%20equation%7D%7D%7BP%3D%5Ccfrac%7B2%7D%7B3%7D%2824%29%2B1%7D%5Cimplies%20P%3D16%2B1%5Cimplies%20%5Cboxed%7BP%3D17%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7BEquilibrium%7D%7B%2824%2C17%29%7D~%5Chfill)
Answer
The answer to your question is 2 x 2 x 5 x 5 or 2² 5²
Step-by-step explanation:
Process
1.- To find the prime factors of a number, we must divide the number by prime numbers like 2, 3, 5, 7, 11, etc. starting from the lowest number.
100 2
50 2
25 5
5 5
1
Then 100 = 2 x 2 x 5 x 5 or 2² 5²
Answer:
44,750
Step-by-step explanation:
4% 35,800=4/100=1/4 then a 1/4 of 35,800=8,950 then add35,800 and 8,950 =44,750 answer
She will have to pay $5,704 in social security taxes.
-In order to find 6.2% of 92,000 you have to multiply .062 * 92,000. This will get you $5,704.
