# Thread: apps using equations with fractions

1. ## apps using equations with fractions

can anyone help me with these problems?

1. what number can be added to both the numerator and the denominator of (16/37) to produce a fraction equal to (5/8)? To answer this question, let x be the number in question. what fraction is produced when x is added to both the numerator and the denominator of (16/37)?

write an equation that says that this fraction is equal to (5/8).

solve this equation for x.

2. A wire 60 inches long is cut into two pieces whose lengths have a ratio of 3 to 1. to find the length of each piece, let x be the length for the shorter piece. since the wire is 60 inches long, and since the shorter piece is x inches long, what is the length of the longer piece?

write a formula that represents the length of the longer piece divided by the length of the shorter piece (that is, a formula for the ratio in terms of x.)

write an equation that says the ratio is equal to (3/1.)

solve this equation for x.

what is the length of each piece?

3. The ratio of the measures of two complementary angles is 4 to 1. find the measure of each angle.

2. Originally Posted by icecreamfrk09
can anyone help me with these problems?

1. what number can be added to both the numerator and the denominator of (16/37) to produce a fraction equal to (5/8)? To answer this question, let x be the number in question. what fraction is produced when x is added to both the numerator and the denominator of (16/37)?

write an equation that says that this fraction is equal to (5/8).

solve this equation for x.

$\frac{16+x}{37+x}=\frac{5}{8}.$

Now solve for $x.$

3. can you please show me how to solve for x because i dont know what steps to do for this problem

4. Originally Posted by icecreamfrk09
can you please show me how to solve for x because i dont know what steps to do for this problem
The method to use is called "cross-multiplying:"

$8(16+x)=5(37+x).$

In other words, you multiply the denominator of one fraction by the numerator of the other, and vice versa.

Now carry out the multiplication, gather like terms, and you should get an equation of the form

$x=$ [answer].

5. okayy does x=19?

6. Originally Posted by icecreamfrk09
okayy does x=19?
Yes, good work!

You can also check the answer by substituting your value of x into the original equation.

Someone else will have to help you with the others. I am off to bed!

Cheers.

7. okayy thank you so much for your help

8. 2. A wire 60 inches long is cut into two pieces whose lengths have a ratio of 3 to 1. to find the length of each piece, let x be the length for the shorter piece. since the wire is 60 inches long, and since the shorter piece is x inches long, what is the length of the longer piece?

write a formula that represents the length of the longer piece divided by the length of the shorter piece (that is, a formula for the ratio in terms of x.)

write an equation that says the ratio is equal to (3/1.)

solve this equation for x.

what is the length of each piece?
If x is the length of the shorter piece, then the length of the longer piece is 60 - x. The equation would then be
$\frac{60 - x}{x} = \frac{3}{1}$
Solve for x.

3. The ratio of the measures of two complementary angles is 4 to 1. find the measure of each angle.
Two angles are complementary if their sum equals 90 degrees. Set up the same way as in the 2nd problem. If angle x is the smaller angle, then what is the larger angle? What would the equation look like, then?

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