Ben and Carmella want to go to a basketball game. Carmella proposes they use a bag of 90 lettered tiles to decide who will pay f
or the tickets. Of the tiles, 35 are vowels and the rest are consonants. She will blindfold Ben and ask to him randomly choose a tile. If Ben picks a vowel, Carmella will pay for the tickets. If Ben picks a consonant, he will pay for the tickets.
Carmella distributes the 90 tiles into two boxes that are located to the left and to right of Ben. She tells Ben that there are a total of 43 lettered tiles in the box on his left, and 43 of the tiles in the box on his right are consonant tiles. Carmella gives Ben three options of how to select his tile.
Method 1: choose randomly from the box on his right
Method 2: choose randomly from the box on his left
Method 3: mix the letter tiles back together, and choose randomly from the entire set of tiles
Use this information to complete the statement.
The probability that Carmella will pay for the tickets is greatest, approximately __%, if Ben selects his tile using method __.
Carmella distributes the 90 tiles into two boxes that are located to the left and to right of Ben. She tells Ben that there are a total of 43 lettered tiles in the box on his left, and 43 of the tiles in the box on his right are consonant tiles. Carmella gives Ben three options of how to select his tile.
Method 1: choose randomly from the box on his right
Method 2: choose randomly from the box on his left
Method 3: mix the letter tiles back together, and choose randomly from the entire set of tiles
Use this information to complete the statement.
The probability that Carmella will pay for the tickets is greatest, approximately __%, if Ben selects his tile using method __.
2 answers:
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<u>ANSWER: </u>
170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution to obtain 1870 liters of 60% solution.
<u>SOLUTION: </u>
First, set up a table. Fill in the unknowns with variables x and y. The table is attached below
From this, we can easily set up the two equations.
Sum of values of two acids = Value of mixture
0.1x + 0.65y = 1122
For convenience, we'll multiply the entire equation by 100,
10x + 65y = 112200 ------ (1)
Now, Sum of amounts of each acid = Amount of mixture
x + y = 1870 ---------(2)
multiply (2) with 10 for easy calculation and derive the equation into one variable.
10x + 10y = 18700
Subtracting equation (2) from (1),
( + ) 10x + 65y = 112200
( − ) 10x + 10y = 18700
we get the solution as,
0 + 55y = 93500
Thus, 55y = 93500
y = 1700
Substituting y = 1700 in (2),
x + 1700 = 1870
x = 1870 - 1700
x = 170
So, we have x = 170 and y = 1700
We can conclude that 170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution to obtain 1870 liters of 60% solution.
