13.15 ounces of 72% acid and 71.85 ounces of 25% acid are needed
<u>Step-by-step explanation:</u>
Total mass of acid required= 85 ounces
Let the mass of 72% acid be 'a'
Let the mass of 25% acid be 'b'
a + b = 85
b = 85-a
85(40/100) = a(72/100) + b(25/100)
85(2/5) = a(72/100) +(85- a) (25/100)
34 = (72a/100) + (2125/100) - (25a/100)
34 - (2125/100) = (72a + 25a) /100
(3400-2125)/100 = 97a /100
97a = 1275
a = 13.15 ounces
b = 85 - 13.14
b = 71.85 ounces
13.15 ounces of 72% acid and 71.85 ounces of 25% acid are needed
Answer:
1 7/8
Step-by-step explanation:
1/4=2/8
2+2/8-3/8= 1 7/8
Multiply both sides of the second equation by 100 to get rid of the decimals:
0.05<em>n</em> + 0.10<em>d</em> = 1.50
==> 5<em>n</em> + 10<em>d</em> = 150
Multiply both sides of the first equation by -5:
<em>n</em> + <em>d</em> = 21
==> -5<em>n</em> - 5<em>d</em> = -105
Add the two equations together:
(5<em>n</em> + 10<em>d</em>) + (-5<em>n</em> - 5<em>d</em>) = 150 + (-105)
Notice that the terms containing <em>n</em> get eliminated and we can solve for <em>d</em> :
(5<em>n</em> - 5<em>n</em>) + (10<em>d</em> - 5<em>d</em>) = 150 - 105
5<em>d</em> = 45
<em>d</em> = 45/5 = 9
Plug this into either original equation to solve for <em>n</em>. Doing this with the first equation is easiest:
<em>n</em> + 9 = 21
<em>n</em> = 21 - 9 = 12
So Donna used 12 nickels and 9 dimes.
Answer:
Each goal gives 5 points and a penalty costs 7 points.
Step-by-step explanation:
Let a penalty cost = x points
And a goal gives = y points
Ben makes 7 goals and 2 penalties ending the game with 21 points,
7y - 2x = 21 --------(1)
Alyssa makes 10 goals and 8 penalties ending the game with (-6) points,
10y - 8x = -6
5y - 4x = -3 --------(2)
Equation (1) multiplied by 2, then subtracted from equation (2),
(5y - 4x) - 2(7y - 2x) = -3 - 2(21)
5y - 4x - 14y + 4x = -3 - 42
-9y = -45
y = 5
From equation (1)
7(5) - 2x = 21
35 - 2x = 21
2x = 35 - 21
2x = 14
x = 7
Therefore, each goal gives 5 points and a penalty costs 7 points.
Answer:
the answer will be 8
Step-by-step explanation:
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