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Svetlanka [38]
3 years ago
6

Everyday, Dave eats either a sandwich or pizza for lunch. Over 42 days, Dave had pizza 3 times for every 4 times he had a sandwi

ch. Over the next x days, he had pizza 3 times for every 2 times he had a sandwich. If at the end of this entire period he had pizza as many times as he has a sandwich, what is the value of x? Please explain.
Mathematics
1 answer:
Elenna [48]3 years ago
5 0

Remark

This problem drove 4 of us crazy until one of us made a break through.


Assumptions.

He must eat either 1 pizza a day or 1 sandwich a day. He can't eat 2 of anything during 1 day. So he can't eat 2 pizzas in a day or 2 sandwiches in a day.


Step One

Find the number of days in a cycle.

3 out of 4 days means out of 4 days he chooses Pizza

2 out of 3 days means out of 3 days he chooses a Sandwich.

That means that there are 4 + 3 days in total = 7 days in the cycle.


Step Two

Find the number of Pizzas and the number of Sandwiches he had during the 42 day period.


3/7 * 42 = Pizzas

3*6 = 18 pizzas in 42 days.


4/7* 42 = Sandwiches

4*6 = 24 sandwiches.


In 42 days he ate 24 + 18 = 42 lunches of either pizzas or sandwiches.


Step three This is the key step.

Find the ratio of sandwiches and pizzas for x days.


Every 5 days he either has 3 pizzas or 2 sandwiches. If the total number of days is x then

3/5 * x = Pizzas

2/5 * x = Sandwiches.


Step 4

Equate the results.

Pizzas = sandwiches.

18 + 3/5 x = 24 + 2/5 x Multiply by 5

18*5 + (3/5)*x * 5 = 24 * 5 + (2/5)*x*5

90 + 3x = 120 + 2x Subtract 2x from both sides

90 + 3x - 2x = 120

90 + x = 120 Subtract 90 from both sides.

x = 120 - 90

x = 30 days.


Conclusion

It takes 30 days to even up the number of pizzas with the number of sandwiches.




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Answer:

2h 1' 1"

Step-by-step explanation:

1h = 1 hora

1' = 1 minute

1" = 1 secind

The sum of the three days is:

  58'  45"

+ 40'  40"

  20'  36"

= 118'  121"

118' 121" = 118' + 121"

1' = 60"

121" = 120" + 1"  = (120/60) + 1 = 2' + 1"

Then:

118' + 121" = 118' + 2' ´+ 1" = 120' + 1"

1 h = 60'

(120/60) + 1 = 2h + 1'

then:

118' + 121" = 2h + 1' + 1"

= 2h 1' 1"

3 0
1 year ago
If James earned 90% on a test and got 36 points, how many points did he lose from the total possible points?
SIZIF [17.4K]

Answer:

4

Step-by-step explanation:

90 percent is 9/10 of total possible

x = total possible points

x * 9/10 = 36

x = 36 * (10/9) = 4 * 10 = 40

40 - 36 = 4

8 0
2 years ago
Read 2 more answers
Rhada has a 6-pound bag of day . Her craft project requires 6 ounces of clay for each batch of 3 ornaments,
kirill [66]

Answer:

Rhada can make 48 ornaments if she uses all of the clay.

Step-by-step explanation:

The complete question is:

Rhada has a 6-pound bag of day . Her craft project requires 6 ounces of clay for each batch of 3 ornaments. If she uses all of the clay, how many ornaments can Rhada make?

Solution:

The amount of clay Rhada has, <em>X</em> = 6-pound.

Convert the weight of clay bag into ounces as follows:

1 pound = 16 ounces

6 pound = 16 × 6

              = 96 ounces.

So, Rhada has 96 ounces of clay.

It is provided that her craft project requires 6 ounces of clay for each batch of ornaments.

Compute the number of batches that can be made by 96 ounces of clay as follows:

Number of batches = Total weight of clay ÷ Amount required for each batch

                                =\frac{96}{6}\\=16

Thus, Rhada can make 16 batches of ornaments.

Now, it is also provided that each batch has 3 ornaments.

Compute the number of ornaments in 16 batches as follows:

Number of ornaments = Number of batches × No. of ornament in 1 batch

                                     =16\times 3\\=48

Thus, Rhada can make 48 ornaments if she uses all of the clay.

3 0
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Answer:

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