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
SpyIntel [72]
3 years ago
9

Tony and Cleo are donating some of their books to a hospital. If Tony contributes half of his books and Cleo gives one third of

hers, they will donate a total of 30 books. If tony gives two fifths of his books and Cleo contributes half of hers, they will donate a total of 31 books. How many books does each have?
Mathematics
1 answer:
liraira [26]3 years ago
4 0
Short Answer: Tony 40 Cleo 30
Givens

T = Tony
C = Cleo

Equations
1/2 T + 1/3 C = 30      (1)
2/5 T + 1/2 C = 31       (2)

Adjustments
Multiply  (1) by 3
Multiply (2) by 2

New Equations
3/2 T + C = 90      (1a)
<u>4/5 T + C = 62</u>      (2a) Subtract (2a) from (1a)
(3/2 - 4/5)T = 28                      the common multiple of 2 and 5 = 10. 
(15/10 - 8/10)T = 28
7/10 T = 28                              Multiply by 10
7T = 28*10
7T = 280  Divide by 7
T = 280/7 = 40

Put T = 40 into (1)
1/2 T + 1/3 C = 30
1/2 (40) + 1/3 C = 30
20 + 1/3 C = 30                      Subtract 20 from both sides.
1/3 C = 30 - 20
1/3 C = 10                              Multiply through by 3
C = 10 * 3
C = 30

Answer:
Cleo has 30 books.
Tony has 40 books.

Check
<em>Use Equation 2</em>
2/5 T + 1/2 C = 31
2/5*40 + 1/2 * 30 = ? 31
16 + 15 =?3`
31 = 31 They are equal.

You might be interested in
HELP PLZ PLZ PLZ!!! Maths
TiliK225 [7]

these inequalities can be solved just like equations

a. x - 7 > 25

+ 7 +7 x > 32the number line would have a filled in circle at 32 with an arrow pointing to the rightb. x - 8 < 5+8 +8x < 13 the number line would have an empty circle at 13 with an arrow pointing to the leftc.x + 11 > 23 - 11 - 11x > 12the number line would have an empty circle at 12 with an arrow pointing to the rightd. x + 12 < 6 - 12 - 12 x < -6the number line would have a filled in circle at -6 with an arrow pointing to the lefta. 21 < x + 18 -18 -18 3 < xx > 3b. 16 < x - 7 + 7 + 7 23 < x x > 23c. 12 > x - 7 + 7 + 7 19 > x x < 19d. 29 < x + 53 - 53 - 53 -24 < x x > -24e. 15 > x + 19 -19 -19 -4 > x x < -4f. 35 > x - 8 +8 +8 43 > x x < 43g. -6 < x - 18 +18 +18 12 < x x > 12h. -15 < x - 2 + 2 +2 -13 < x x > -13
3 0
3 years ago
Your city is having a sneaker convention! A pair of Ground Morgans is 20% less expensive than a pair of Elite Butterflies, Elite
Amanda [17]

Answer:

Ground Morgans are 52% the price of Floating Jumps.

Step-by-step explanation:

A pair of Ground Morgans GM is 20% less expensive than a pair of Elite Butterflies EB, this means

GM= 0.8 EB <em>(GM is 80% the price of EB's)</em>

Elite Butterflies EB are 30% more expensive than Cloud Trainers CT's, this means

EB =1.3 CT <em>(EM's is 130% the price of CT's)</em>

Cloud Trainers CT are 50% less expensive than Floating Jumps FJ, this means

CT=0.5FJ <em>(CT is 50% the price of FJ)</em>

Now, if we want the price of Ground Morgans in terms of Floating Jumps, then, since EB = 1.3 CT,

GM=0.8 (1.3CT)

and since CT = 0.5F, we have

GM = 0.8(1.3(0.5FJ)).

Simplifying we get

\boxed{GM =0.52FJ}

Ground Morgans are 52% the price of Floating Jumps.

5 0
3 years ago
In 2012, there were about 313 million people in the United States, and just under 9 million of them had assets of $1 million or
zloy xaker [14]
New York has a density of millionaires more than twice that of the country as a whole. The density of millionaires is about the same for New York City as for the United States. Millionaires seem to prefer New York City to much of the rest of the United States. There is something in the water of New York City that encourages millionaires
3 0
3 years ago
Two bowls of pasta at a restaurant serve 3 people. How many bowls of pasta should be ordered for 12 people?
Butoxors [25]
12 people divided by 3 people = 4

so if 2 bowls serve 3 people...2 bowls x 4 = serve 12 people

therefore, 8 bowls serve 12 people
6 0
3 years ago
Read 2 more answers
How much is 25 centimeters in meters
Olegator [25]
0.25 meter is the answer
5 0
3 years ago
Read 2 more answers
Other questions:
  • 11.
    12·2 answers
  • 275 per 60 sec divided by 7
    6·1 answer
  • 9x + 10(6x-1) Please Help solve
    15·1 answer
  • -9x-4x Combining Like Terms and Evaluating Algebraic Expressions Activity
    12·1 answer
  • A recipe calls for 2/3 cup of flour for every 4 teaspoons of vanilla. How much vanilla should be used for every 1 cups of flour?
    11·1 answer
  • Plz help me on number 4
    9·1 answer
  • What did the Election say after fixing a light bulb at the top of a empire building
    9·1 answer
  • A rocket carrying fireworks is launched from a hill 80 feet above a lake. The rocket will fall into lake after exploding at its
    9·1 answer
  • Which pairs of polygons are similar?<br> Select each correct answer
    5·1 answer
  • Lashonda made $95 for 5 hours of work.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!