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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.




You might be interested in
Calcule:<br> a)-400-(-700)=
Juliette [100K]

-400-(-700)

-140+700

= 300


I hope that's help ! If you have question(s) please let me know



8 0
3 years ago
Two metal disks, one with radius r = 2. 50 cm and the other with radius r = 5. 00 cm are welded together and
vova2212 [387]

The total moment of inertia of the two disks will be I = 2.375 × 10-³ Kgm² welded together to form one unit.

<h3>What is moment of inertia?</h3>

Moment of inertia is the quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.

Using the formulas to calculate the moment of inertia of a solid cylinder:

I = ½MR²

Where;

I = moment (kgm²)

M = mass of object (Kg)

R = radius of object (m)

Total moment of inertia of the two disks is expressed as: I = I(1) + I(2)

That is;

I = ½M1R1 + ½M2R2

According to the provided information;

R1 = 2.50cm = 0.025m

M1 = 0.800kg

R2 = 5.00cm = 0.05m

M2 = 1.70kg

I = (½ × 0.800 × 0.025²) + (½ × 0.05² × 1.70)

I = (½ × 0.0005) + (½ × 0.00425)

I = (0.00025) + (0.002125)

I = 0.002375

I = 2.375 × 10-³ Kgm²

Hence The total moment of inertia of the two disks will be I = 2.375 × 10-³ Kgm² welded together to form one unit.

To know more about moment of inertia follow

brainly.com/question/14460640

#SPJ4

4 0
2 years ago
Systems of linear equations ; elimination method<br><br><br> pls help&lt;3
Basile [38]
<h3>Answer:</h3>

System

  • 10s +25t = 11700
  • s -2t = 0

Solution

  • s = 520
  • t = 260
<h3>Explanation:</h3>

Let s and t represent single-entry and three-day tickets, respectively. These variables represent the numbers we're asked to find: "how many of each [ticket type] he sold."

We are given the revenue from each ticket type, and the total revenue, so we can write an equation based on the relation between prices, numbers sold, and revenue:

... 10s +25t = 11700 . . . . . equation for total revenue

We are also given a relation between the two number of tickets sold:

... s = 2t . . . . . . . . . . . . . . . twice as many single tickets were sold as 3-day

We can rearrange this second equation to put it into standard form. That makes it easier to see what to do to eliminate a variable.

... s -2t = 0 . . . . . . . . . . . . subtract 2t to put into standard form

So, our system of equations is ...

  • 10s +25t = 11700
  • s -2t = 0

<em>What </em>elimination<em> is all about</em>

The idea with "elimination" is to find a multiple of one (or both) equations such that the coefficients of one of the variables are opposite. Then, the result of adding those multiples will be to eliminate that variable.

Here, we can multiply the second equation by -10 to make the coefficient of s be -10, the opposite of its value in the first equation. (We could also multiply the first equation by -0.1 to achieve the same result. This would result in a non-integer value for the coefficient of t, but the solution process would still work.)

Alternatively, we can multiply the first equation by 2 and the second equation by 25 to give two equations with 50t and -50t as the t-variable terms. These would cancel when added, so would eliminate the t variable. (It seems like more work to do that, so we'll choose the first option.)

<em>Solution by elimination</em>

... 10s +25t = 11700 . . . . our first equation

... -10s +20t = 0 . . . . . . . second equation of our system, multiplied by -10

... 45t = 11700 . . . . . . . . .the sum of these two equations (s-term eliminated)

... t = 11700/45 = 260 . . . . . divide by the coefficient of t

... s = 2t = 520 . . . . . . . . . . use the relationship with s to find s

_____

<em>Solution using your number sense</em>

As soon as you see there is a relation between single-day tickets and 3-day tickets, you can realize that all you need to do is bundle the tickets according to that relation, then find the number of bundles. Here, 2 single-day tickets and 1 three-day ticket will bundle to give a package worth 2×$10 + $25 = $45. Then the revenue of $11700 will be $11700/$45 = 260 packages of tickets. That amounts to 260 three-day tickets and 520 single-day tickets.

(You may notice that our elimination solution effectively computes this same result, where "t" and the number of "packages" is the same value (since there is 1 "t" in the package).)

6 0
3 years ago
2 Which graph shows a proportional relationship? a b c d ​
Harrizon [31]

Answer:

x xjjkdjbdnnxuhxnmdujxnxlxuxbx

6 0
2 years ago
Very confusing not sure
Arturiano [62]

Answer:

This describes a translation.

8 0
3 years ago
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