Solve the proportions. (Solve for x)
1. 3x/7 = 8/21
2. 20/10 = x+2/5
1. To solve the proportion 3x/7 = 8/21 for x, cross multiply by multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa:
(3x)(21) = (7)(8)
Simplify the equation:
63x = 56
To solve for x, divide both sides of the equation by 63:
x = 56/63
Simplify the fraction:
x = 8/9
Therefore, the solution to the proportion 3x/7 = 8/21 is x = 8/9.
2. To solve the proportion 20/10 = (x + 2)/5, you can cross multiply as well:
(20)(5) = (10)(x + 2)
Simplify the equation:
100 = 10x + 20
Subtract 20 from both sides of the equation:
100 - 20 = 10x
Simplify:
80 = 10x
To solve for x, divide both sides of the equation by 10:
x = 80/10
Simplify:
x = 8
So, the solution to the proportion 20/10 = (x + 2)/5 is x = 8.
To solve the proportions, you can use a property of proportions which states that the cross products of a proportion are equal. This means that if you have a proportion a/b = c/d, then ad = bc.
Let's solve the given proportions step by step:
1. 3x/7 = 8/21
First, we can cross-multiply:
(3x)(21) = (7)(8)
Simplifying both sides:
63x = 56
Now, divide both sides by 63 to solve for x:
x = 56/63
Simplifying further:
x = 8/9
2. 20/10 = x+2/5
Again, cross-multiply:
(20)(5) = (10)(x+2)
Simplifying both sides:
100 = 10x + 20
Next, subtract 20 from both sides:
100 - 20 = 10x
Simplifying further:
80 = 10x
Finally, divide both sides by 10:
80/10 = x
Simplifying:
8 = x
So, x = 8.
Therefore, the solutions to the given proportions are:
1. x = 8/9
2. x = 8
3x = 7*8/21
x+2 = 5*20/10
That should get you started