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vitfil [10]
3 years ago
8

A store is having a sale on DVDs and CDs. DVDs cost $4 and CDs cost $7. On one day, the store made $204 from DVD and CD sales, a

nd sold a total of 39 items. Write a system of equations, then solve to find how many DVDs and CDs were sold.
Mathematics
1 answer:
Gre4nikov [31]3 years ago
4 0
We are given here the individual costs of DVD and CD as well as the total sales and the number of items sold on one day. To solve the number of DVDs and CDs sold each, we devise two independent linear equations:

(1) x + y = 39
(2) 4x + 7y = 204

x- number of DVDs; y - number of CDs

solving, x= 23 DVDs
y = 16 CDs

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4. You are traveling to Chicago for a job interview. You leave Toledo, Ohio, at 5:45 A.M. and arrive in Elkhart, Indiana, at 8:1
Dvinal [7]

Answer:

48 mph

Step-by-step explanation:

First we need to find the distance from Elkhart to Chicago. Toledo to Elkhart is 136 miles and Toledo to Chicago 244 miles.

So the distance from Elkhart to Chicago can be calculated, since Chicago is farther from Toledo than Elkhart, as: distance(Toledo to Chicago) - distance(Toledo to Elkhart). These distances are given in the problem, so the distance from Elkhat to Chicago is: 244 miles - 136 miles = 108 miles.

This problem basically wants to know the slowest you can be yet still ariving on time. If you are the minimum speed, you will arrive in Chicago exactly at 10:30 A.M. So you have 2 hours and 15 minutes(10:30 A.M - 8.15A.M.) to drive 108 miles.

15 minutes is a fourth of a hour, so you have 2.25hours to go through 108 miles.

The minimum speed you must maintain is 108mph/2.25h = 48mph.

5 0
3 years ago
Ashwin helps paint a square mural in his classroom. Then he helps paint a mural in the hallway whose length is 7 feet longer and
Serhud [2]

Ashwin paints 2 murals:

  1. A square mural in his classroom
  2. A mural in the hallway with length 7 feet longer and width 3 feet shorter

Also, x indicates the side length of the mural in the classroom. Since the classroom mural is square in shape, the length and breadth of the mural would be x.

Part A: Expression to represents the two binomials to be multiplied to find the area of the hallway mural

Area of the hallway mural = Length of the hallway mural × Breadth of the hallway mural

So Length of the hallway mural = Length of the classroom mural + 7

⇒ Length of the hallway mural = x + 7

Breadth of the hallway mural = Breadth of the classroom mural - 3

⇒ Breadth of the hallway mural = x - 3

Hence, x + 7 and x - 3 need to be multiplied to determine the area of the mural

Part B: Area of the hallway mural

Area of the hallway mural = Length of the hallway mural × Breadth of the hallway mural

⇒ Area of the hallway mural = (x + 7) × (x-3)

⇒ Area of the hallway mural = x² + 7x - 3x - 21

⇒ Area of the hallway mural = x² + 4x - 21

Part C: Area of the hallway mural if each side of the classroom mural is 8 foot long

Putting the value x = 8 in the answer of Part B

⇒ Area of the hallway mural = 8² + 4×8 - 21

⇒ Area of the hallway mural = 64 + 4×8 - 21

⇒ Area of the hallway mural = 64 + 32 - 21

⇒ Area of the hallway mural = 75 square feet


3 0
3 years ago
Read 2 more answers
Point A is located at (5, 10) and point B is located at (20, 25).
Alla [95]
Let's say the point is C, so C partitions AB into two pieces, where AC is at a ratio of 3 and CB is at  a ratio of 7, thus 3:7,

\bf \left. \qquad  \right.\textit{internal division of a line segment}
\\\\\\
A(5,10)\qquad B(20,25)\qquad
\qquad 3:7
\\\\\\
\cfrac{AC}{CB} = \cfrac{3}{7}\implies \cfrac{A}{B} = \cfrac{3}{7}\implies 7A=3B\implies 7(5,10)=3(20,25)\\\\
-------------------------------\\\\
{ C=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\
-------------------------------

\bf C=\left(\cfrac{(7\cdot 5)+(3\cdot 20)}{3+7}\quad ,\quad \cfrac{(7\cdot 10)+(3\cdot 25)}{3+7}\right)
\\\\\\
C=\left( \cfrac{35+60}{10}~~,~~\cfrac{70+75}{10} \right)\implies C=\left(\cfrac{95}{10}~~,~~\cfrac{145}{10}  \right)
\\\\\\
C=\left( \cfrac{19}{2}~~,~~\cfrac{29}{2} \right)\implies C=\left( 9\frac{1}{2}~~,~~14\frac{1}{2}  \right)
8 0
3 years ago
Identify the property used in the first five steps to solve the equations (2x-5)-6x=-22
Bad White [126]
Combine like terms
Add to both sides
Divide both sides
I only see three steps, man
4 0
3 years ago
In ΔRST, the measure of ∠T=90°, the measure of ∠R=82°, and TR = 44 feet. Find the length of ST to the nearest tenth of a foot.
yuradex [85]

Answer: 313.1 feet

Step-by-step explanation:

\tan 82=\frac{x}{44}

tan82=

44

x

​

44\tan 82=x

44tan82=x

x=313.0763\approx \mathbf{313.1}\text{ feet}

x=313.0763≈313.1 feet

4 0
3 years ago
Read 2 more answers
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