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3 years ago

Two fractions have denominators 4 and 6. Their sum is 19/12

Mathematics

1 answer:

Viefleur [7K]3 years ago

5 0

The value of numerators are 3 and 5

Solution:

Let the numerators of two fractions be x and y

Two fractions have denominators 4 and 6. Their sum is 19/12

Therefore,

$\frac{x}{4} + \frac{y}{6} = \frac{19}{12}$

Cross multiply L.H.S to get simplified

$\frac{6x+4y}{24} = \frac{19}{12}\\\\6x + 4y = 38 ------- eqn 1$

If the numerators are switched their sum is 7/4

Therefore,

$\frac{y}{4} + \frac{x}{6} = \frac{7}{4}$

On simplification, we get

$\frac{6y + 4x}{24} = \frac{7}{4}\\\\4x + 6y = 42 -------- eqn 2$

Solve eqn 1 and eqn 2

Multiply eqn 1 by 4

24x + 16y = 152 --------- eqn 3

Multiply eqn 2 by 6

24x + 36y = 252 ---------- eqn 4

Subtract eqn 3 from eqn 4

24x + 36y = 252

24x + 16y = 152

( - ) -------------------

20y = 100

Substitute y = 5 in eqn 1

6x + 4(5) = 38

6x = 38 - 20

6x = 18

Thus the value of numerators are 3 and 5

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3. As part of your weight training regimen, you want to consume lean sources of protein. You want consume at least 300 Calories

erastova [34]

Answer:

Let x ounce of chicken and y ounce of tofu were taken,

∵ One ounce of chicken provides 35 Calories and 8.5 g of protein,

So, in x ounces of chicken

Calories = 35x, Protein = 8.5x grams,

Now, One ounce of tofu provides 20 Calories and 2.5 g of protein.

So, in y ounces of tofu,

Calories = 20y and protein = 2.5y grams,

Thus, the total calories = 35x + 20y,

Total protein = 8.5x + 2.5y

According to the question,

35x + 20y ≥ 300 -----(1),

8.5x + 2.5y ≥ 48 ----(2),

Now, the cost of a pound for chicken = $ 5,

So, the cost of 16 ounces of chicken = $ 5 ( ∵ 1 pound = 16 ounces ),

⇒ the cost of 1 ounces of chicken = $\frac{5}{16}$ dollars,

Similarly, the cost of a pound of tofu = $ 2.5,

So, the cost of 1 ounces of tofu = $\frac{2.5}{16}$ dollars,

Thus, the total cost of x ounces of chicken and y ounces of tofu

$C=\frac{5}{16}x+\frac{2.5}{16}y$

Now, by graphing the above constraints ( by equation (1) and (2) )

We get a feasible region that shows the possible values of x and y,

The boundary points of the feasible region are,

(2.545, 10.545), (0, 19.2), (8.571, 0)

$C=\frac{5}{16}\times 2.545+\frac{2.5}{16}\times 10.545 = 2.443$

$C=\frac{5}{16}\times 0+\frac{2.5}{16}\times 19.2 = 3$

$C=\frac{5}{16}\times 8.571+\frac{2.5}{16}\times 0 = 2.678$

Hence, the minimum cost is $ 2.443,

For which 2.545 ounces of chicken and 10.545 ounces of tofu should be eaten.

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A quarterback is standing in the middle of the field 60 yards from his goal line. He passes the ball to a player 12 yards to his

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So for this you would have to use the pythagorean theorem which is α²+b²=c². The 12 yards would be a and the distance between the 60 yard line and 50 yard line which is 5 would be b and you would be trying to find out what c is.

a²+b²=c²
12²+5²=c²
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now you want to get c alone and in order to do that we would square root it and i'm sure you have learned that what you do on one side you have to do to the other so we would also square root 169
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hope i helped :)

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