answer.
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
zalisa [80]
2 years ago
15

A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens an

d pencils were purchased if there were 80 more pencils than pens?
Mathematics
1 answer:
Mkey [24]2 years ago
6 0

Answer:

  • <u>120 pens and 200 pencils.</u>

<u></u>

Explanation:

You can set a system of two equations.

<u>1. Variables</u>

<u />

  • x: number of pens
  • y: number of pencils

<u>2. Cost</u>

  • <em>each pen costs</em> $1, then x pens costs: x
  • <em>each pencil costs</em> $0.5, then y pencil costs: 0.5y

  • Then, the total cost is: x + 0.5y

  • The cost of the whole purchase was $ 220, then the first equation is:

          x + 0.5y = 220 ↔ equation (1)

<u>3. </u><em><u>There were 80 more pencils than pens</u></em>

Then:

  pencils  =      80   +   pens

       ↓                               ↓

       y        =      80   +      x        ↔ equation (2)

<u>4. Solve the system</u>

i) Substitute the equation (2) into the equation (1):

  • x + 0.5(80 + x) = 220

ii) Solve

  • x + 40 + 0.5x = 220
  • 1.5x = 180
  • x = 180/1.5
  • x = 120 pens

iii) Substitute x = 120 into the equation (2)

  • y = 80 + 120
  • y = 200 pencils

Solution: 120 pens and 200 pencils ← answer

You might be interested in
There are 90 sixth graders at Wilson Middle School. Only 50% of the sixth graders will attend the morning assembly. How many six
SVETLANKA909090 [29]

Answer: 45


Step-by-step explanation:

Divide 90 by 2 and you will the the answer of 45.

7 0
2 years ago
Read 2 more answers
In the 2000 presidential election, three candidates split the vote as follows:
Lera25 [3.4K]

Answer:

c 23 and 0.46 are statistics and 0.484 is a  parameter

True. For this case the value 0.46 represent t statistic since from the sample obtained we can calculate the sample proportion of people who voted for Gore like this:

\hat p_{Gore]=\frac{X}{n}=\frac{23}{50}=0.46

Where X represent the people with the characteristic desired in the random sample selected.

So then we can say that 23 and 0.46 represent statistics since comes from the sample. And the value 0.484 is obtained from the population so then represent a parameter.  

Step-by-step explanation:

Previous concepts

A parameter is any "numerical quantity that characterizes a given population or some aspect of it". For this case we are interested on proportions and we denote the population proportion by p

A statistic is "used to estimate the value of a population parameter". In other words is just an estimation of the population parameter of interest. Four our case the sample proportion denoted by \hat p represent the statistic for this case.

Solution for the problem

a 0.46 and 0.484 are statistics

False. 0.484 is not an statistic since it's the outcome from the original population and would represent the parameter "proportion of people who vote for Gore"

b 50 and 23 are statistics and 0.484 is a  parameter

False. The sample size is not an statistic is just a value selected in order to calculate the statistic.

c 23 and 0.46 are statistics and 0.484 is a  parameter

True. For this case the value 0.46 represent t statistic since from the sample obtained we can calculate the sample proportion of people who voted for Gore like this:

\hat p_{Gore]=\frac{X}{n}=\frac{23}{50}=0.46

Where X represent the people with the characteristic desired in the random sample selected.

So then we can say that 23 and 0.46 represent statistics since comes from the sample. And the value 0.484 is obtained from the population so then represent a parameter.  

6 0
2 years ago
Which of these r-values represents the weakest correlation? A.-0.55 B -0.45 C -0.25 D -0.35
irakobra [83]
The smaller the magnitude of the correlation, the weaker the correlation.  The magnitude of -0.25 is 0.25, the smallest correlation magnitude.  
6 0
2 years ago
This is harder so i put more points
Inessa [10]

Answer:

Sheet metal costs <u>$20</u> per square foot.

Step-by-step explanation:

7.6x - 2.3x = 106

We are finding the value of x.

5.3x = 106

Divide both sides by 5.3.

x = 106 ÷ 5.3

x = 20

3 0
1 year ago
Read 2 more answers
Solve the system of equations.<br> - 5x + 2y = 9
Marina CMI [18]

Answer: -5x + 2y -9 = 0

Step-by-step explanation:

1. Move constant to the left and change its sign

2. Change the signs on both sides of the equation

3 0
2 years ago
Other questions:
  • The line L1 has equation 2x+y=8.The line L2 passes through the point A(7,4) and is perpendicular to L1.
    5·1 answer
  • Eric has challenged himself to walk 24,000 steps in 4 days. If Eric walks the same number of steps each day, which function repr
    5·1 answer
  • m∠3 is (3x + 4)° and m∠5 is (2x + 11)°. Angles 3 and 5 are . The equation can be used to solve for x. m∠5 = °
    15·2 answers
  • The graph of which function has a minimum located at (4, –3)?
    6·2 answers
  • Bob wants to plant a 7 foot by 10 foot garden with a uniform border of petunias around the outside and still have 28 square feet
    11·2 answers
  • A simple random sample (SRS) of 100 of a certain popular car in 1997 found that 20 had a certain minor defect in the brakes. An
    13·1 answer
  • 23% of U.S adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the
    13·1 answer
  • A half melon is approximated by the region between two concentric spheres, one of radius a and the other of radius with くa &lt;
    14·1 answer
  • What is the sum of StartRoot negative 2 EndRoot and StartRoot negative 18 EndRoot?
    12·2 answers
  • Oscar drew the image of a
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!