Simplify {(1/3)^-2 -(1/2)^-2 } / (1/4)^-2

Margo brought 7 pens from a book store some pens cost $3.00 EACH and the rest cost $4.00 . If she paid a total of 23.00 for the

Montano1993 [528]

Answer:

5

Step-by-step explanation:

Margo bought 7 pens for $23.

Some pens are $3 and some $4.

We need to find how many $3 pens she bought.

Let the number of $3 pens be represented by p and let the number of $3 pens be represented by r. So:

p = $3 and r = $4

Now we know 7 pens were purchased so is we add the number of $3 pens purchased to the number of $4 pens purchased, we will get 7.

p + r = 7

We know that the total cost of the pens is $23 so that equation would be found by takign the $3 pen multiplied by the number of $3 pens purchsed added to the $4 pen multiplied by the number of $4 pens purchsed, which equals $23.

$3p + $4r = $23

Now we have 2 equations and 2 unknowns.

p + r = 7

$3p + $4r = $23

Let's solve for r in the first equation.

p + r = 7 Subtract p from both sides.

p - p + r = 7 - p The p on the left cancels.

r = 7 - p

Now that we know r, we can substitute it into the second equation and solve for p.

$3p + $4r = $23

3p + 4( 7 - p) = 23 Multiply it out.

3p + 4*7 - 4*p = $23

3p + 28 - 4p = 23 Combine like terms.

3p - 4p + 28 = 23

- 1p + 28 = 23 Subtract 28 from both sides.

- p + 28 - 28 = 23 - 28

- p = - 5 Divide each side by -1

- p/- 1 = - 5/ - 1 The negative cancels on each side.

p = 5

We can see Margo bought 5 $3 pens.

For fun, let's solve for how many $4 pens she bought. We know p, so we plug it in the first equation and solve for r.

p + r = 7

5 + r = 7 Subtract 5 from each side

5 - 5 + r = 7 - 5

r = 7 - 5

r = 2

So Margo bought 5 $3 pens and 2 $4 pens!

8 0

2 years ago

Beverley has quarters and dimes in her pocket. She has 21 coins with a total value of $3.00. How many of each type of coin does

kondaur [170]

Answer:

Step-by-step explanation:

If all 21 coins were dimes, she'd have $2.10. But she has 90 more cents than that. Now for each coin that's a quarter, not a dime, she has 15 cents more. 90/15= 6. So there are 6 quarters, and 21-6 = 15 dimes.

Now we do it backwards to see if it's right. 6 quarters is $1.50, 15 dimes is $1.50, add those together and you get $3. So it's right. 6 quarters, 15 dimes.

6 0

2 years ago

Dado dos ángulos complementarios, uno mide (2x + 10) y el otro (x + 20),

rusak2 [61]

Answer:

El valor de x es igual a 20 o x = 20.

Step-by-step explanation:

Lo primero que se debe saber es que dos ángulos complementarios suman un ángulo recto o 90º.

Supongamos que el valor de un ángulo $\\ \alpha$ y un ángulo $\\ \beta$ valen:

$\\ \alpha = 2x + 10$ [1]

$\\ \beta = x + 20$ [2]

Como la suma de $\\ \alpha + \beta = 90$ [3]

Entonces

$\\ \alpha + \beta = (2x + 10) + (x + 20) = 90$

Sumamos los factores comunes entre si:

$\\ (2x + x) + (10 + 20) = 90$

Para la primera expresión debemos recordar que se suman sólo los coeficientes. Así:

$\\ (2 + 1)x + (10 + 20) = 90$

$\\ 3x + 30 = 90$

Para despejar la incógnita x, debemos tener en cuenta que una igualdad no se altera si se suma, se resta, se multiplica o divide un mismo valor a cada lado de ella. Por esta razón, para despejar 3x, lo primero que podemos hacer es sumar -30 a cada lado de la expresión (lo que es igual a restar 30 a cada lado de la misma). Así tenemos:

$\\ 3x + 30 - 30 = 90 - 30$