Given :
A bag with 2 ½ ounces of peanuts can make ⅔ of a jar of peanut butter.
To Find :
How many ounces of peanuts will it take for there to be one jar of peanut butter.
Solution :
![2\dfrac{1}{2}\ ounces = \dfrac{2}{3}\ jar\\\\\dfrac{5}{2}\ ounces = \dfrac{2}{3}\ jar\\\\1= \dfrac{15}{4}\ \dfrac{ounces}{jar}](https://tex.z-dn.net/?f=2%5Cdfrac%7B1%7D%7B2%7D%5C%20ounces%20%3D%20%5Cdfrac%7B2%7D%7B3%7D%5C%20jar%5C%5C%5C%5C%5Cdfrac%7B5%7D%7B2%7D%5C%20ounces%20%3D%20%5Cdfrac%7B2%7D%7B3%7D%5C%20jar%5C%5C%5C%5C1%3D%20%5Cdfrac%7B15%7D%7B4%7D%5C%20%5Cdfrac%7Bounces%7D%7Bjar%7D)
Now,
1 jar of peanut butter is made by :
![1\times jar \times \dfrac{15}{4} \dfrac{ounces}{jar}\\\\\dfrac{15}{4}\ ounces](https://tex.z-dn.net/?f=1%5Ctimes%20jar%20%5Ctimes%20%5Cdfrac%7B15%7D%7B4%7D%20%5Cdfrac%7Bounces%7D%7Bjar%7D%5C%5C%5C%5C%5Cdfrac%7B15%7D%7B4%7D%5C%20ounces)
Hence, this is the required solution.
Divide the amount saved by the original price then multiply by 100 to get the percent:
6/40 = 0.15
0.15 x 100 = 15%
4(4a 7 ) 3(2a 5) = 4 ( 4 x 5 x 7 ) x 3 ( 2 x 5 x 5 ) = 560 x 150 = 84000
For this case we have the following quadratic equation:
![3x ^ 2 + 13x + 5 = 0](https://tex.z-dn.net/?f=3x%20%5E%202%20%2B%2013x%20%2B%205%20%3D%200)
Where:
![a = 3\\b = 13\\c = 5](https://tex.z-dn.net/?f=a%20%3D%203%5C%5Cb%20%3D%2013%5C%5Cc%20%3D%205)
Applying the quadratic formula:
![x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-b%20%5Cpm%20%5Csqrt%20%7Bb%20%5E%202-4%20%28a%29%20%28c%29%7D%7D%20%7B2a%7D)
Substituting the values:
![x = \frac {-13 \pm \sqrt {13 ^ 2-4 (3) (5)}} {2 (3)}\\x = \frac {-13 \pm \sqrt {169-60}} {6}\\x = \frac {-13 \pm \sqrt {109}} {6}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-13%20%5Cpm%20%5Csqrt%20%7B13%20%5E%202-4%20%283%29%20%285%29%7D%7D%20%7B2%20%283%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-13%20%5Cpm%20%5Csqrt%20%7B169-60%7D%7D%20%7B6%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-13%20%5Cpm%20%5Csqrt%20%7B109%7D%7D%20%7B6%7D)
Thus, we have two roots:
![x_ {1} = \frac {-13- \sqrt {109}} {6} = - 3.91\\x_ {2} = \frac {-13+ \sqrt {109}} {6} -0.43](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%5Cfrac%20%7B-13-%20%5Csqrt%20%7B109%7D%7D%20%7B6%7D%20%3D%20-%203.91%5C%5Cx_%20%7B2%7D%20%3D%20%5Cfrac%20%7B-13%2B%20%5Csqrt%20%7B109%7D%7D%20%7B6%7D%20-0.43)
Answer:
![x_ {1} = - 3.91\\x_ {2} = - 0.43](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20-%203.91%5C%5Cx_%20%7B2%7D%20%3D%20-%200.43)