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
strojnjashka [21]
3 years ago
10

John and will also ran for Middle School council president. There are 90 students voting in middle school. If the ratio of Will'

s votes to John's votes are the same how many vo
Mathematics
1 answer:
lesya692 [45]3 years ago
4 0

Hi!

This problem is the fifth in a series of seven about ratios. At first glance the problem may look to be beyond 6.RP.1, which limits itself to “describe a ratio relationship between two quantities. However, even though there are three quantities (the number of each candidates' votes), they are only considered two at a time.

In the first problem students define the simple ratios that exist among the three candidates. It opens an opportunity to introduce unit rates.

The subsequent problems are more complex. In the second problem, students apply their understanding of ratios to combine two pools of voters to determine a new ratio. In the third problem, students apply a known ratio to a new, larger pool of voters to determine the number of votes that would be garnered.

Solutions

Solution: Question #1

a. John's votes to Will's, 16 to 8, or 2 to 1. Marie's votes to Will's, 12 to 8, 3 to 2, or 32 to 1, the unit ratio. Marie's votes to John's, 12 to 16, 3 to 4, or 34 to 1, the unit ratio.

Solution: Question #2

2. Will now has 8 + 12 = 20 votes to John's 16 votes, so the ratio of Will's votes to John's votes is 20 : 16, 5 : 4, or 54 : 1, the unit ratio.

Solution: Question #3 - Computing votes

There are different ways to approach this problem, but both begin with the fact that Will gets votes in a 5 to 4 ratio compared with John and require recognizing that a 5 to 4 ratio means a total of 9 equal parts. Then it is straightforward to compute:

59×90=50 votes for Will

49×90=40 for John

50−40=10 more votes for Will.

Solution: Question #3 - Applying fractions

One can solve the problem by working fractions by recognizing that Will getting votes in a 5 to 4 ratio means a total of 9 equal parts. It follows that Will gets 59 of the 90 votes and John gets 49 of the 90 votes:

59−49=19 of the voters

19×90=10 more votes for Will

Solution: Question #3 - Equivalent Ratios

An alternate very basic solution to Question 3 involves creating a series of equivalent ratios. This approach may be selected by students who are still developing an understanding of proportional situations. Students may begin with the ratio of 5 to 4 and proceed to find a ratio such that the sum of numerator and denominator is 90. This sequence may appear as follows:

5/4 = 10/8 = 15/12 = 20/16 = 25/20 = 30/24 = 35/28 = 40/32 = 45/36 =50/40

Then 50 - 40 = 10 more votes for Will

Overall answer

10 more votes for will

You might be interested in
Parallel to y=2/3x+6 through (-3, 6)
Lana71 [14]

Answer:

y = (2/3)x + 8

Step-by-step explanation:

Parallel lines have the same slope. In the given equation, the slope is 2/3 so the slope of the parallel line will also be 2/3.

y = (2/3)x + ?

Plug in (-3, 6) for (x, y) in the equation.

6 = (2/3)(-3) + ?

6 = -2 + ?

? = 8

Final equation: y = (2/3)x + 8

7 0
3 years ago
Does this mean that A is the home or????
alexira [117]
Where the line segment A starts is home
8 0
3 years ago
The graphs of f(x)=-2x and g(x)=(1/2)^x are shown. what are the solutions to thr equation -2x=(1/2)^x? select each correct answe
sineoko [7]

Answer:

<h2>-2</h2>

Step-by-step explanation:

hello :

f(x)=-2x and g(x)=(1/2)^x

f(-2)=-2(-2) =4

g(-2)=(1/2)^-2 = 1/2^-2 = 2²=4

4 0
3 years ago
3 times a number is 54 less than the square of that number. Find the negative solution.
Pavel [41]

Answer:

x=-6

Step-by-step explanation:

Let x be the number

3x = x^2 -54

Subtract 3x

3x-3x = x^2 -3x-54

0 = x^2 -3x-54

Factor

What 2 numbers multiply to -54 and add to -3

-9*6 = -54

-9+6 = -3

0=(x-9) (x+6)

Using the zero product property

x-9=0    x+6=0

x=9  x=-6

The questions asks for the negative solution

x=-6

3 0
3 years ago
Eddie has a globe that he is going to unfold and lay flat to hang on the wall as a map. If the radius of the globe is 22.5 cm, w
nirvana33 [79]

Answer:

B. 6358.5 square centimeters. This is right.

5 0
3 years ago
Other questions:
  • Two trains leave stations 324 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour
    7·1 answer
  • The volume (v) of a sphere varies directly as the cube of its diameter (d). Write this statement in algebraic language, using an
    14·2 answers
  • The sum of the first 666 terms of a geometric series is 15{,}62415,62415, comma, 624 and the common ratio is 555.
    5·1 answer
  • A scale drawing for a rectangular parking lot measures 6 cm by 12 cm. The scale is 5 cm: 25 m. Find the area of the parking lot.
    13·1 answer
  • HELP PLZ THIS IS DUE TODAY
    10·1 answer
  • I neeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd
    14·1 answer
  • Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each sale
    12·2 answers
  • What is the slope in the equation: y=4x+3<br>​
    13·1 answer
  • Change 3/8 to percent
    9·1 answer
  • 3 b. A taxi hurries 261 km in 135 minutes. What is its average speed in kilometers per hour?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!