Ask question

Ask question

All categories

3 years ago

15

Sasha has some pennies, nickels, and dimes in her pocket. The number of coins is 16. The expression 0.01p+0.05n+0.10d represents

the value of the coins, which is $1.22. She has twice as many nickles as pennies. How many of each coin does Sasha have?

1 answer:

uysha [10]3 years ago

3 0

I would like to use cents

p+n+d=16
1p+5n+10d=122
twice as many nicklese a pennies, n=2p

sub 2p for n
p+2p+d=16
1p+5(2p)+10d=122
simplified
3p+d=16
1p+10p+10d=122

3p+d=16
11p+10d=122
now solve
use subsitution

3p+d=16
minus 3p from both sides
d=16-3p
sub 16-3p for d in other equation

11p+10(16-3p)=122
11p+160-30p=122
160-19p=122
minus 160 both sides
-19p=-38
divide both sides by -19
p=2

sub back
n=2p
n=2(2)
n=4

d=16-3p
d=16-3(2)
d=16-6
d=10

2 pennies
4 nickles
10 dimes

You might be interested in

56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

$\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2$

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ <em> </em> $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

8 0

2 years ago

If you can travel 500 miles in 1 hour, how long will it take you to travel 800 miles

zhenek [66]

Answer:

1 hours and 30 minutes

Step-by-step explanation:

7 0

3 years ago

Solve using order of operations (9 + 33 – 6 ) ÷ 6 – 32

marusya05 [52]

Answer:

-26

Step-by-step explanation:

9+33-6

calculate the sum of the positive numbers

42-6

subtract the numbers

36 divided by 6-32

6-32

-26

5 0

2 years ago

Read 2 more answers

There is a raffle at a hockey game and 125 tickets are sold. Maris bought 3 tickets. What percent of the tickets

Alina [70]

Answer:

2.4%

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

What is the median of the following set of numbers? 33, 30, 29, 28, 27, 34, 31

IrinaVladis [17]

Median is a middle value
So it is 28

4 0

3 years ago

Read 2 more answers