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2 years ago

9

a dance club spent $922 on 40 items.The item include some hats and pairs of shoes.Each hat cost $19 and each pair of shoes cost

$25.How many pairs of shoes did the dance club buy?

1 answer:

Sergio039 [100]2 years ago

4 0

1. H+S=40

2. 19H+25S=922

From 1,

19H+19S=760

Subtract this from 2 to eliminate H,

19H+25S-19H-19S=922-760

6S=162

Solve for S, then use either equation to solve for H.

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Justin weighs 15 pounds less than Greg weighs. Half of Greg’s weight is 75 pounds less than Justin’s weight. How much does each

sp2606 [1]

Lets take Gregs weight as “x”. This means that Justins weight is x-15, and x/2 = (x-15)-75.

If we take that last equation, lets combine like terms:

x/2 = x - 15 - 75
x/2 = x - 90
Now multiply both sides by 2 to get rid of the fraction
x = 2x - 180
Subtract 2x from both sides
x - 2x = -180
-x = -180
x = 180 — this is Gregs weight

Justins weight is x-15, so 180-15, which is 165 pounds. Hope this helped.

5 0

2 years ago

three positive numbers are in Arithmetic Progression (A.P). the sum of the squares of the three numbers is 155. while the sum of

Alecsey [184]

Given:
Three numbers in an AP, all positive.
Sum is 21.
Sum of squares is 155.
Common difference is positive.

We do not know what x and y stand for. Will just solve for the three numbers in the AP.
Let m=middle number, then since sum=21, m=21/3=7
Let d=common difference.
Sum of squares
(7-d)^2+7^2+(7+d)^2=155
Expand left-hand side
3*7^2-2d^2=155
d^2=(155-147)/2=4
d=+2 or -2
=+2 (common difference is positive)

Therefore the three numbers of the AP are
{7-2,7,7+2}, or
{5,7,9}

6 0

2 years ago

A firm has a revenue function that can be represented by r (x)=700x-0.35x^2, where r (x) is the total revenue (in dollars) and x

Fudgin [204]

Answer:

How many units need to be sold to produce the maximum revenue? 1000 units

How many in dollars is the maximum revenue when the maximum of units are sold? $350,000

Step-by-step explanation:

We get max value of a function if we differentiate it and set it equal to 0.

We need to differentiate r(x) and set it equal to 0 and solve for x.

<u><em>That would be number of units sold to get max revenue.</em></u>

<u><em /></u>

<u>Then we take that "x" value and substitute into r(x) to get the max revenue amount.</u>

<u />

Before differentiating, we see the rules shown below:

$f(x)=ax^n\\f'(x)=n*ax^{n-1}$

Where

f'(x) is the differentiated function

Now, let's do the process:

$r (x)=700x-0.35x^2\\r(x)=700-2*0.35x\\r(x)=700-0.7x\\0=700-0.7x\\0.7x=700\\x=1000$

So, 1000 units need to be sold for max revenue

Now, substituting, we get:

$r (x)=700x-0.35x^2\\r(1000)=700(1000)-0.35(1000)^2\\r(1000)=350,000$

The max revenue amount is $350,000

5 0

2 years ago

Jinghua hiked 4 1/2 miles through the woods in 2 1/4 hours. She hiked the return trip at the same average rate but by a differen

Anna007 [38]

Answer:

5 miles.

Step-by-step explanation:

Consider the question: Jinghua hiked 4 1/2 miles through the woods in 2 1/4 hours. She hiked the return trip at the same average rate but by a different route taking 2 1/2 hours. How many miles did Jinghua hike on the return trip ?

First of all, we will find Jinghua's speed using given information as:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Convert mixed fractions into improper fractions:

$4\frac{1}{2}\Rightarrow \frac{9}{2}$

$2\frac{1}{4}\Rightarrow \frac{9}{4}$

$\text{Jinghua's speed}=\frac{\frac{9}{2}\text{ Miles}}{\frac{9}{4}\text{ Hours}}$

Using property $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}$ :

$\text{Jinghua's speed}=\frac{9*4\text{ Miles}}{9*2\text{ Hours}}$

$\text{Jinghua's speed}=\frac{2\text{ Miles}}{\text{ Hour}}$

We know that distance is equal to the product of speed and time.

$\text{Distance}=\text{Speed}\times\text{Time}$

Since we have been given that Jingua hiked the return trip at the same average rate, so distance covered by her on return trip would be speed (2 miles her hour) times given time (2 1/2 hours).

$\text{Distance covered by Jingua on return trip}=\frac{2\text{ Miles}}{\text{ Hour}}\times 2\frac{1}{2}\text{ Hours}$

$\text{Distance covered by Jingua on return trip}=2\text{ Miles}\times \frac{5}{2}$

$\text{Distance covered by Jingua on return trip}=5\text{ Miles}$

Therefore, Jingua hiked 5 miles on her return trip.

8 0

2 years ago

£399 is shared between Ann, Bill, Chloe and Dave.

tiny-mole [99]

Answer is 4.5 Show all
Steps below

6 0

2 years ago