1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
wel
3 years ago
11

At a fundraiser breakfast, the bill for three glasses of orange juice and five pancake specials is $7.60, whereas the bill for o

ne glass of orange juice and two pancake specials is $2.90. The system of equation {(3j [email protected] 2p=2.90)┤ represents this situation, where j represents the cost of a glass of orange juice and p represents the cost of a pancake special. What would be the bill for one glass of orange juice and one pancake special?
Mathematics
2 answers:
Readme [11.4K]3 years ago
7 0
We have a system of equation:
3j + 5p= $7.60 (1)
j + 2p= $2.90 (2)

Multiply equation (2) by 3:
3j + 6p = $8.70 (3)

Take (3)- (1), we have:
(3j) - (3j) + (6p - 5p) = $8.70- $7.60
⇒ p= $1.10

Now, we use equation (2) to find j:
j= $2.90- 2* $1.10
⇒ j= $0.70

j+ p= $0.70 + $1.10= $1.80

The bill for one glass of orange juice and one pancake special would be $1.80.

Hope this helps~



Marizza181 [45]3 years ago
3 0
Ok, so you are looking for the price of the orange juice and the pancake special individually. So, the first step is to declare our variables: 

<span>j = price of the orange juice. </span>
<span>p = price of the pancake special. </span>

<span>So the first bill, translated with our variables is </span>
<span>3j + 5p = 7.60 </span>

<span>The second bill, translated with our variables is </span>
<span>1j + 2p = 2.90 </span>

<span>Now, it says to use the substitution method, so we need to solve one of those equations for one variable. Since in the second equation, we have one term with a coefficient of 1, that will be the easiest to solve for. So we move everything other than that term to the other side. </span>

<span>1j = 2.90 - 2p </span>

<span>Now we have j solved for, we will substitute it into the other equation </span>

<span>3(2.90 - 2p) + 5p = 7.60 </span>

<span>Now we have only one variable, so we just simplify </span>

<span>8.70 - 6p + 5p = 7.60 </span>
<span>-1p = -1.10 </span>
<span>p = 1.10 </span>

<span>Now we know how much the pancake special costs, we can plug this into either of the two original equations and solve for the price of the orange juice. </span>

<span>1j + 2(1.10) = 2.90 </span>
<span>j = 0.70 </span>

<span>Now part c asks for the cost of one orange juice and one pancake special. So, with our variables, that will be: </span>
<span>j + p </span>

<span>We already know the values of these variables, so we can plug them in. </span>

<span>0.70 + 1.10 = $1.80 </span>

<span>2) Linear combination is the same as the addition/elimination method. This means your goal is to add the equations together. But before we do that, we want to multiply one row by some random number so that when we add the rows together, we can get rid of one of the variables. </span>

<span>a - 2b = 2 </span>
<span>a - 1b = 6 </span>

<span>So we have two choices here. We can multiply one of the a's by -1 to make it negative. That way one of them is positive, and the other is negative, and they will cancel when we add them together. OR we can multiply the bottom equation by -2. This will make the b variable in the bottom row a +2b and it will cancel out with the -2b in the top equation. </span>

<span>Both will give you the right answer, so it won't matter which way you go. Since it's a smaller number, I'm going to go with the first way, and multiply the top a by -1. </span>

<span>Note: You need to multiply EVERYTHING in the equation by the number! </span>

<span>-1(1a - 2b = 2) </span>
<span>a - b = 6 </span>

<span>-a + 2b = -2 </span>
<span>a - b = 6 </span>

<span>When you add the rows together, simply add like terms. Notice the a will cancel out. The +2b will add with the -b to make 1b and the -2 will add with the 6 to make 4 </span>

<span>So we have: </span>

<span>1b = 4 </span>

<span>And now we can go back up and plug this info in to solve for the other variable </span>

<span>a - (4) = 6 </span>
<span>a = 10</span>
You might be interested in
You worked theses hours this week: 1 1/2 , 2 3/4, 3 3/4, 5 1/2
alukav5142 [94]

Answer: 13.5 hours.

I got the answer by simply adding up the integers to start with.

Integers = 1, 2, 3 and 5.

The integers added up equal to 11.

Next we add up the remaining fractions.

Fractions = 1/2, 3/4, 3/4 and 1/2.

We can add up 1/2 and 1/2 to equal 1, and 3/4 and 3/4 to make 1.5.

1 + 1.5 = 2.5          

Finally, we add up the answer for the integers and the fractions together, (11 + 2.5) which equals 13.5.

Our answer is 13.5 hours.      

(Not sure why the answer isn't in the choices)                          

6 0
3 years ago
Help!! Answer !!! about to run out of time in test!!
Gemiola [76]

\qquad \qquad\huge \underline{\boxed{\sf Answer}}

Here's the solution ~

Let's find the measure of hypotenuse first, by using Pythagoras theorem ;

\qquad \sf  \dashrightarrow \: h {}^{2}  =  {8}^{2}  +  {6}^{2}

\qquad \sf  \dashrightarrow \: h {}^{2}  =  {36}^{}  +  {64}^{}

\qquad \sf  \dashrightarrow \: h {}^{2}  = 100

\qquad \sf  \dashrightarrow \: h {}^{}  =  \sqrt{100}

\qquad \sf  \dashrightarrow \: h {}^{}  =  {10}

Now, let's find the asked values ~

\qquad \sf  \dashrightarrow \:  \sin(x) =  \dfrac{opposite \: side}{hypotenuse}

\qquad \sf  \dashrightarrow \:  \sin(x) =  \dfrac{6}{10}

\qquad \sf  \dashrightarrow \:  \sin(x) =  \dfrac{3}{5}   \: or \: 0.6 \: units

For Cos y :

\qquad \sf  \dashrightarrow \:  \cos(y) =  \dfrac{adjcant \: side}{hypotenuse}

\qquad \sf  \dashrightarrow \:  \cos(y)   = \dfrac{6}{10}

\qquad \sf  \dashrightarrow \:  \cos(y)   = \dfrac{3}{5}  \: or \: 0.6 \: units

As we can see that both sin x and Cos y have equal values, therefore The required relationships is equality.

I.e Sin x = Cos y

Hope it helps ~

3 0
2 years ago
A recipe calls for 2/3 cup of milk for 11 cookies. How many cups of milk are needed for 165 cookies​
gavmur [86]

Answer:

11 x 15 = 165, so to make 165 cookies, you would need 15 times the milk.

2/3 times 15 = 10

You would need 10 cups of milk to make 165 cookies

7 0
2 years ago
Read 2 more answers
In RST, m R =(2x+10)°, m 5=(2x+25)°, and m T=(x-5)°.
cricket20 [7]

We know that : Sum of Angles in a Triangle is equal to : 180°

⇒ In ΔRST, The Sum of Angles ∠R , ∠S , ∠T should be equal to 180°

⇒ m∠R + m∠S + m∠T = 180°

⇒ (2x + 10)° + (2x + 25)° + (x - 5)° = 180°

⇒ (2x + 2x + x) + (10° + 25° - 5°) = 180°

⇒ 5x + 30° = 180°

⇒ 5x = 180° - 30°

⇒ 5x = 150°

⇒ x = 30°

5 0
3 years ago
A teenager’s heart pumps an average of 7200 L of blood every 24 hours. What is the rate of change of volume of blood?
love history [14]

Answer:

300L per hour

Step-by-step explanation:

The rate of change of volume of blood pumped by the teenager's heart expresses the volume of blood pumped with respect to hour.

Rate of change of volume of blood = \frac{volume of blood}{time}

                           = \frac{7200L}{24}

                           = 300L/hour

The rate of change of volume of blood by the teenager's heart is 300 litres per hour. This implies that his/ her heart pumps 300 litres of blood every hour.

7 0
3 years ago
Other questions:
  • Mark deposited $9,000 into two saving accounts bearing simple interest. One of the accounts has an interest rate of 8% while the
    9·1 answer
  • the area of the mojave desert is 25,000 square miles. A scale drawing of the mojave desert has an area of 10 square inches. What
    14·1 answer
  • (6v2 + v – 3) 4 - 5v + 7
    7·1 answer
  • Identify the domain of the function shown in the graph
    10·2 answers
  • special Sophia's Festival Garden is divided into 12 equal sections she plant carrots in 8 of the sections write two fractions th
    7·1 answer
  • Terri has 5 boxes of flower seeds. She wants to give the seeds away to friends. If she gives 1/8 of a box away how many people c
    8·1 answer
  • A miner started at 8 feet above sea level and then traveled 23 feet straight down into a mine shaft. What was the miner's elevat
    15·1 answer
  • What is the volume of the figure shown?
    13·1 answer
  • Graph the equation y=-3x-4 by plotting points
    12·1 answer
  • The diagram shows a 15-meter wire attached to the top of a telephone pole. The wire is attached to the ground at a point 6 meter
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!