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
Andre45 [30]
3 years ago
15

A school is preparing fruit baskets for a local nursing home. There are 162 apples, 108 oranges, and 180 bananas. If the baskets

are identical and there is no leftover fruit, what is the greatest number of baskets that can be made? How many apples, oranges, and bananas are in each basket?
Mathematics
2 answers:
stepan [7]3 years ago
6 0
<span>Number of baskets = 18
 Apples = 9
 Oranges = 6
 Bananas = 10

   For this problem, you need to find the greatest common factor (GCF) of all three numbers. Thankfully, you can do that one pair at a time.
 For 162 and 108, the GCF is 54.
 Then find the GCF of 54 and 180, which is 18.

   Now you know that the greatest number of baskets you can have with all baskets being identical and no fruit left over is 18. To determine how much of each fruit in a basket, simply divide each quantity by 18, so:

   Apples: 162/18 = 9
 Oranges: 108/18 = 6
 Bananas: 180/180 = 10

   Note: One method for determining the GCF of 2 numbers is Euclid's Algorithm which is quite simple: Take 2 positive numbers A and B and calculate C = A mod B. (mod is simply the remainder after performing an integer division. For example 9 mod 3 = 0, 10 mod 3 = 1, 11 mod 3 = 2, 12 mod 3 = 0 and so on). If the result is 0, then B is the GCF of A and B. If the result is not 0, then assign A the value of B, then assign B the value of C and perform the modulo operation again until you finally get a result of 0.

Some examples: 162 mod 108 = 54, 108 mod 54 = 0; Therefore the GCF of 162 and 108 is 54.
 180 mod 54 = 18, 54 mod 18 = 0; Therefore the GCF of 180 and 54 is 18. 210 mod 54 = 48, 54 mod 48 = 6, 48 mod 6 = 0; Therefore the GCF of 210 and 54 is 6.</span>
kari74 [83]3 years ago
3 0

To solve this exercise, we must calculate the Maximum Common Divisor (M.C.D.), which is the greatest common divisor of 62,108 and 180. We apply factor decomposition, and we obtain:

 162= (3^4)(2)

 108= (2^2)(3^3)

 180= (2^2)(3^2)(5)

 We choose the common numbers with their lowest exponent:

 M.C.D.= (2)(3^2)

 M.C.D.= 2x9

 M.C.D.= 18

 The greatest number of baskets that can be made is: 18 baskets

 To know how many apples, oranges and bananas are in each basket, we must divide the greatest number of them that can be made between the total amount of apples, oranges and bananas, as shown below:

 162/18= 9 apples

 108/18= 6 oranges

 180/18= 10 bananas

 So, there are 9 apples, 6 oranges and 10 bananas in each basket.


You might be interested in
What is equivalent to 36/72
AveGali [126]
1/2 because 36 is half of 72. You could also divide the numbers by 12 and you will get 3/6 which is the same as 1/2.
8 0
3 years ago
Read 2 more answers
A pom-pom manufacturer makes each of its pom-poms with 35% white strands (w), 25% blue strands (b), and 40% red strands (r). If
DIA [1.3K]

Answer:

28 white strands , 20 blue strands and 32 red strands are needed to make a pair of pom-poms

Step-by-step explanation:

Given :A pom-pom manufacturer makes each of its pom-poms with 35% white strands (w), 25% blue strands (b), and 40% red strands (r).

To Find : If each pom-pom has a total of 80 strands, how many of strands of each color are needed to make a pair of pom-poms?

Solution:

Total Strands = 80

White Strands = 35%

No. of white strands = 35\% \times 80 =\frac{35}{100} \times 80 =28

Blue Strands = 25%

No. of blue strands = 25\% \times 80 =\frac{25}{100} \times 80 =20

Red Strands = 40%

No. of Red strands = 40\% \times 80 =\frac{40}{100} \times 80 =32

Hence 28 white strands , 20 blue strands and 32 red strands are needed to make a pair of pom-poms

3 0
3 years ago
Read 2 more answers
Helpppppppppp<br> Urgenttttt<br> Pleaseeeee!
Alika [10]

Answer:

The first set is a set of linear equations.

The way to figure this out is pretty easy. If you want to see it visually, go search up desmos graphing calculator and put in these equations.

A linear equation is a function that has a constant slope, meaning that the rate it increases or decreases will never change. The first one is a set of linear equations because it is 2 equations with constant slopes, meaning that the slopes will never change no matter what y and x are.

The second set is not, because while the first equation is linear, the second is an inequality. While it is a straight line, it doesn't count as a linear equation.

The third set, both equations have exponents on the x, which means that the slope will change depending on x. This means that both of these are not linear equations.

The only set that is a linear set is the one that has only linear equations.

3 0
2 years ago
Dave receives a salary of $200 a week plus a commission of 10% of his weekly sales. An equation y = m x + b represents Dave’s we
vovangra [49]

Answer:

y = 0.1x+200

Step-by-step explanation:

First, let's establish that:

x is independent

y is dependent

Basically, the value of y will depend on what x is.

The problem states that the slope of the line is Dave's comission, so since he makes 10% of comission, we can make the slope as 0.1x (mx)

The problem also states that the y intercept (b) is Dave's base salary, and earlier in the problem it states that his base salary is $200 a week. Therefore, b=200

now, the equation is:

y=0.1x+200

Hope this helps!

4 0
3 years ago
Value​ Rent-A-Car rents a luxury car at a daily rate of ​$44.86 plus 50 cents per mile. A business person is allotted ​$100 for
natta225 [31]

Answer:

110.28

Step-by-step explanation:

First: 100 - 44.86 = 55.14

Second: 55.14/.50 = 110.28

Last: The most you can travel is 110.28 miles per day!

Please mark Branilest!


3 0
3 years ago
Other questions:
  • Your dog weighed 42 and eight ninths pounds. The dog gained 3 and one half. You put him on a diet and he lost 6 and seven sixtee
    12·1 answer
  • There are two coins in a bag. for coin 1, p(h) = ½ and for coin 2, p(h) = 1/3. your friend chooses one of the coins at random an
    14·1 answer
  • Roni wants to write an equation to represent a proportional relationship that has a constant of proportionality equal to 7/25. S
    12·2 answers
  • What is the domain of f(x) = -4^2 -4x +2
    13·1 answer
  • Pls help will give brainliest and 5star plss help
    14·2 answers
  • Put 6x-2y=-14 into slope intercept form ( y=mx+b) then graph
    8·1 answer
  • What is 11 - 10 <br> HELP HURRY PLEASE ANSWER QUICK
    8·1 answer
  • 3. How
    5·1 answer
  • Which percent is equivalent to 3/5 ?
    5·2 answers
  • A class is collecting aluminum cans. Every Monday each student brings in a bag with 10 cans. They put 10 bags into a box. How ma
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!