All categories

3 years ago

Abbi has $400 in $5 bills. If she has 38 bills, how many of them are $20?

Mathematics

2 answers:

In-s [12.5K]3 years ago

8 0

$400 in $5 = 80 bills
it says she has 38 bills so she has 20. 400/20= 20

Sergio039 [100]3 years ago

3 0

F=5 dollar bills
t=twent dollar bills

38 total bills
f+t=38

400 in bills
400=5f+20t

we have
f+t=38
5f+20t=400
multipy first equation by -5 and add to second equation

-5f-5t=-190
5f+20t=400 +
0f+15t=210

15t=210

divide both sides by 15
t=14

subsitute
t+f=38
15+f=38
f=23

23 five dolar bills
15 twenty dollar bills

You might be interested in

Find the solutions to the equation below 30x^2-28x+6 =0

Naddik [55]

For this case, we have the following equation of the second degree:

$30x ^ 2-28x + 6 = 0$

If we divide between 2 on both sides of the equation, we will have:

$15x ^ 2-14x + 3 = 0$

Where:

$a = 15\\b = -14\\c = 3$

The solutions will come from:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}$

Substituting:

$x = \frac {- (- 14) \pm \sqrt {(- 14) ^ 2-4 (15) (3)}} {2 (15)}\\x = \frac {14 \pm \sqrt {196-180}} {30}\\x = \frac {14 \pm \sqrt {16}} {30}\\x = \frac {14 \pm4} {30}$

So, we have:

$x_ {1} = \frac{14 + 4} {30} = \frac {18} {30} = \frac {18} {30} = \frac {3} {5}\\x_ {2} = \frac {14-4} {30} = \frac {10} {30} = \frac {1} {3}\\$

Answer:

$x_ {1} = \frac {3} {5}\\x_ {2} = \frac {1} {3}$

Option A

Option E

6 0

3 years ago

Read 2 more answers

A rectangular prism is a three-dimensional geometric figure, hollow or solid, contained by six rectangular sides that meet at ri

jenyasd209 [6]

Answer:B. C. D.

Step-by-step explanation:

8 0

3 years ago

To find the volume of a rectangular prism you multiply the 3 dimensions, length x width x height. What combination of numbers wi

aleksklad [387]

1, 1 and 17. Since 17 is a prime number, there isn’t exactly numbers that are multiplied by each other that give 17.

8 0

2 years ago

Read 2 more answers

A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the

creativ13 [48]

Answer:

$A(\theta)=\frac{162 \theta}{(\theta+2)^2}$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

$2r+s=18$

$s=r \theta$

$2r+r \theta=18$

solve for r

$r=\frac{18}{2+\theta}$

step 2

Find the value of s

$s=r \theta$

substitute the value of r

$s=\frac{18}{2+\theta}\theta$

step 3

we know that

The area of complete circle is equal to

$A=\pi r^{2}$

The complete circle subtends a central angle of 2π radians

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

$\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}$

substitute the value of r

$A=\frac{(\frac{18}{2+\theta})^2\theta}{2}$

$A=\frac{162 \theta}{(\theta+2)^2}$

Convert to function notation

$A(\theta)=\frac{162 \theta}{(\theta+2)^2}$

6 0

4 years ago

A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D (x) = 943 - 17 x, where q is the q

Alex73 [517]

Answer:

See expla below

Step-by-step explanation:

Given the demand function:

q = D (x) = 943 - 17 x

a) Find the elasticity:

Find the derivative of the demand function.

D'(x)= -17

Thus, elasticity expression is:

$\frac{x D'(x)}{D'(x)}$

$= \frac{x (-17)}{943 - 17x}$

$= \frac{17x}{943 - 17x}$

Elasticity expression = $E(x) = \frac{17x}{943 - 17x}$

b) At what price is the elasticity of demand equal to 1?

This means E(x) = 1

Substitute 1 for E(x) in the elasticity equation:

$E(x) = \frac{17x}{943 - 17x}$

$1 = \frac{17x}{943 - 17x}$

Cross multiply:

$943 - 17x = 17x$

Collect like terms

$17x + 17x = 943$

$34x = 943$

$x = \frac{943}{34}$

x = 27.74

Elasticity at the price of demand = 1 is 27.74

c) At what prices is the elasticity of demand elastic?

This means E(x) > 1

Therefore,

$\frac{17x}{943 - 17x} > 1$

Cross multiply:

$17x > 943 - 17x$

Collect like terms

$17x + 17x > 943$

$34x > 943$

$x > \frac{943}{34}$

x > 27.74

The elasticity of demand is elastic at x > 27.74

d) At what prices is the elasticity of demand inelastic?

This means E(x) < 1

Therefore,

$\frac{17x}{943 - 17x} < 1$

Cross multiply:

$17x < 943 - 17x$

Collect like terms

$17x + 17x < 943$

$34x < 943$

$x < \frac{943}{34}$

x < 27.74

The elasticity of demand is inelastic at x < 27.74

e) At what price is the revenue a maximum:

Total revenue will be:

R(x) = x D(x)

= x (943 - 17x)

= 943x - 17x²

R(x) = 934 - 17x(price that maximizes total revenue)

Take R(x) = 0

Thus,

0 = 943 - 17x

17x = 943x

$x = \frac{943}{17}$

$x = 27.74$

Total revenue is maximun at x= 27.74 per cookie

f) At x = 21 per cookie, find the price:

Thus,

R (21) = (943 * 21) - (17 * 21²)

= 19803 - 7497

= 12306

At x = 27.74, find the price:

R(27.74) = (943 * 27.74) - (17 - 27.74²)

= 26158.82 - 13081.63

= 13077.19

We can see the new price of cookie causes the total revenue to decrease.

Therefore, with a small increase in price the total revenue will decrease.

5 0

3 years ago