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
A vertical plane intersects the three-dimensional object in the image and divides the object into equal halves. What is the shap
Crank
If you were to take a knife and cut this shape down the middle, starting from the top, what will the cross section look like? 
It will look a lot like how the object looks from the side.
The best answer is D, the last image. 
7 0
2 years ago
Read 2 more answers
1. tentukan hasil dari 243⅔?
Vesnalui [34]

Penjelasan langkah demi langkah:

1)

= 243^{\frac{2}{3} }\\= (\sqrt[3]{243})^2\\= 7^2\\= 49

2) √32 +3√18-2√50

= √16*2 +3√9*2-2√25*2

= 4√2 + 3(3√2)-2(5√2)

= 4√2 + 9√2-10√2

= 13√2-10√2

= 3√2

3) 1000 ⅔×64⅙

 = (\sqrt[3]{1000}) ^2 \times (2^6)^{1/6}  \\= 10^2 \times 2\\= 100 \times 2\\= 200

4) 3/4+√2

3/4+\sqrt{2} \\= \frac{3+4\sqrt{2} }{4 }

5) 2√3×√18

= 2√3×√9*2

= 2√3×3√2

= (2*3)(√3*√2)

= 6√6

6) 12/3+√3

= 4+√3

7) √1000—2√40

= 10 -2 (√4*10)

= 10-2(2√10)

= 10 - 4√10

8) 2- ¹+3-¹

= \frac{1}{2} + \frac{1}{3}\\ = \frac{3+2}{6}\\ = \frac{5}{6}

9)

\frac{5}{\sqrt{5} }\\ merasionalisasikan\\= \frac{5}{\sqrt{5} }\times \frac{\sqrt{5} }{\sqrt{5} }\\= \frac{5\sqrt{5} }{\sqrt{25} }\\= \frac{5\sqrt{5} }{5}\\ = \frac{\sqrt{5} }{1}

Jika pernyataannya opsional, penyebutnya adalah 1

10) 2√3×√18

= 2√3×√9*2

= 2√3×3√2

= (2*3)(√3*√2)

= 6√6

7 0
2 years ago
If cos(t) = 2/7 and t is in the 4th quadrant, find sin(t).
Yuliya22 [10]
We can use the Pythagorean Trigonometric Identity which says:
sin^2(t)+cos^2(t)=1

Since we need to find sin(t), we have to solve for it:
sin(t)= \sqrt{1-cos^2(t)}

Let's plug in the given cos(t) value:
sin(t) = \sqrt{1-cos^2( \frac{2}{7})}

And solve sin(t):
sin(t) = \sqrt{1- \frac{4}{49} } = \frac{x}{y} \sqrt{ \frac{49}{49}- \frac{4}{49} }

Simplify further:
sin(t) = \sqrt{ \frac{45}{49} } = \frac{ \sqrt{45} }{7} = \frac{ \sqrt{9*5} }{7}

And it all simplifies down to:
sin(t) = \frac{3 \sqrt{5} }{7}

Since it's in the 4th quadrant, the sin(t) value is going to be negative. So, your final answer is: 
sin(t) = - \frac{ 3\sqrt{5} }{7}

Hope this helps!
7 0
2 years ago
Please help me!!!!!!!!!!
bezimeni [28]
9.2 x 13.8 = 126.96, now usually to get the area of a triangle we would half this but because we have two of the same triangle we would then have to double it again so they cancel each other out. We then do 6.9 x 9.2 which equals 63.48 and again we have two of the same triangle so no need to half it. So we add the two totals of 126.96 and 63.48 together to get 190.44.
4 0
2 years ago
Given right triangle ABC which of the following statements must be true? Check all that apply.
Pachacha [2.7K]

Answer:

Option A. <A and <B are complementary angles

Option D. Sin(C)=Cos(90\°-C)

Step-by-step explanation:

we know that

If ABC is a right triangle

then

------> by complementary angles

and

Sin(C)=Cos(A)

Cos(C)=Sin(A)

Remember that

A=90\°-C

so

Sin(C)=Cos(90\°-C)

Cos(C)=Sin(90\°-C)

5 0
2 years ago
Other questions:
  • A) A box contains 50 diodes of which 10 are known to be bad. A diode is selected at random. What...
    12·1 answer
  • A computer program contains one error. In order to find the error, we split the program into 6 blocks and test two of them, sele
    5·1 answer
  • How much of a 90% alloy must be combined with 70% gold alloy in order to get 60 ounces of an 85% gold alloy?
    15·1 answer
  • Bridgette opened a store credit card to purchase a business suit for $463. She put the entire purchase on the credit card. Her A
    15·1 answer
  • Lincoln and Hunter work at a dry cleaners ironing shirts. Lincoln can iron 30 shirts per hour, and Hunter can iron 20 shirts per
    13·1 answer
  • Lindsey bought a new candle and the base of the candle covers an area of 19.625 square inches. She plans on putting the candle i
    14·2 answers
  • ) It has been estimated that 53% of all college students change their major at least once during the course of their college car
    8·1 answer
  • A sumo wrestling ring is circular and has a circumference of 4.6\pi \text{ meters}4.6π meters4, point, 6, pi, start text, space,
    7·1 answer
  • 3x18 = 3 (10+8) is an example of the _________ property of multiplication.
    6·1 answer
  • Problem: It takes 1200 workers 8 years to build 3 ziggurats. How many years would It take 1600 workers to build 25 ziggurats? ​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!