Let
x = number of liters of the 40% salt solution
y = number of liters of the 20% salt solution
The two amounts (x and y) must combine to 1500 liters, so
x+y = 1500
we can solve for y to get
y = 1500-x
after subtracting x from both sides
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If we have x liters of the 40% salt solution (composed of pure salt plus other stuff) then we have exactly 0.40*x liters of pure salt. Simply multiply the decimal form of the percentage with the amount of solution.
Similarly, if we have y liters of the 20% solution, then we have 0.20*y liters of pure salt
Combined, we have 0.40*x + 0.20*y liters of pure salt all together.
We want 1500 liters of a 28% solution, so we want 1500*0.28 = 420 liters of pure salt
Equate the two expressions (0.40*x + 0.20*y and 420) to get
0.40*x + 0.20*y = 420
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We have the equation 0.40*x + 0.20*y = 420 and we also know that y = 1500-x
Let's use the substitution property now
0.40*x + 0.20*y = 420
0.40*x + 0.20*( y ) = 420
0.40*x + 0.20*( 1500 - x ) = 420 ... note how y is replaced with 1500-x
Now we can solve for x
0.40*x + 0.20*( 1500 - x ) = 420
0.40*x + 0.20*(1500) + 0.20*(-x) = 420
0.40*x + 300 - 0.20x = 420
0.40*x - 0.20x + 300 = 420
0.20x + 300 = 420
0.20x + 300 - 300 = 420 - 300
0.20x = 120
0.20x/0.20 = 120/0.20
x = 600
Now that we know x, use this to find y
y = 1500-x
y = 1500-600 ... plug in x = 600 (ie replace x with 600)
y = 900
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Answers:
We need 600 liters of the 40% solution
We need 900 liters of the 20% solution
1.)
x + (x + 1) = 145
2x + 1 = 145
2x = 145 - 1
2x = 144
x = 72
if x is equal to 72
72 + 1 = 73
therefore the 2 integers is 72 and 73
2.
x + (x + 1) + (x + 2) = 54
3x + 3 = 54
3x = 54 - 3
3x = 51
x = 17
numbers are, 17, 18 and 19
Answer:
the girls be 12 and boys be 48 respectively
Step-by-step explanation:
The computation of the number of boys and number of girls is shown below:
Let us assume A be girls
And, b be boys
According to the question
b = 4 × a
b - 8 = 2 × (a + 8)
b - 8 = 2 × a + 16
4 × a -8 = 2 × a + 16
4 × a - 2 × a = 16 + 8
2 × a = 24
a = 12
Now
b = 4 × a
= 4 × 12
= 48
Hence, the girls be 12 and boys be 48 respectively
The answer is 8.5
Hope this helped
