This is a typical mixture problem where using a table is the best thing.
pints juice % juice = total % juice
juice A x .70 = .70x
juice B 60-x .95 = .95(60-x)
total 60 .75 = 60(.75)

The last row gives you a total that you need to use, so do that multiplication to get 45. You now to need to add the last columns together for rows 1 and 2 and set them equal to 45: .7x +.95(60-x) = 45. When you do that math, you'll get that x = 48. This means that you need 48 pints of juice A and 60-48 pints of juice B, which is 12 pints.

6 0

2 years ago

In a group of 40 people, 27 can speak English and 25 can speak Spanish. How many can speak

Svetradugi [14.3K]

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Information \: provided \: with \: us }}}}}\: \bigstar}$

➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{What \: we \: have \: to \: find ? }}}}}\: \bigstar}$

➻ The required number of people who can speak both English and Spanish .

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Assumption}}}}}\: \bigstar}$

<u>Consider</u> ,

➻ A → Set of people who speak English.

➻ B → Set of people who speak Spanish

➻ A∩B → Set of people who can speak both English and Spanish

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Given}}}}}\: \bigstar}$

➻ n (A) = 27

➻ n (B) = 25

➻ n (A∪B) = 40

➻ n(A∩B) = ?

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Now}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - n (A∩B)

➻ 40 = 52 - n (A∩B)

➻ n (A∩B) = 52 - 40

➻ ∴ n (A∩B) = 12

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Therefore}}}}}\: \bigstar}$

∴ Required Number of persons who can speak both English and Spanish are <u>12 .</u>

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$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Verification}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - 12

➻ 40 = 52 - 12

➻ 40 = 40

➻ ∴ L.H.S = R.H.S

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6 0

2 years ago