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3 years ago

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Mrs. Smith took her family and friends to the movies. There was a total of 15 people. Child tickets cost 5$ and adult tickets co

st 10$. She spent a total of 110$. How many adults went to the movies? Children?

1 answer:

SCORPION-xisa [38]3 years ago

3 0

Answer: children= 8, adult= 7

Step-by-step explanation:

Let the number of children be x

Let the number of adults be y

There was a total of 15 people. This can be represented as:

x + y = 15 .......... equation i

Child tickets cost 5$ and adult tickets cost 10$. She then spent a total of 110$. This can be represented as:

5x + 10y = 110 ............. equation ii

Combine both equations

x + y = 15 ........... equation i

5x + 10y = 110 .......... equation ii

Multiply equation I by 5

Multiply equation ii by 1

5(x + y = 15)

1(5x + 10y = 110)

5x + 5y = 75 .......... equation iii

5x + 10y = 110 ........ equation iv

Subtract equation iv from iii

-5y = -35

y = 35/5

y = 7

Number of adults is 7

Since x + y = 15

x = 15 - 7

x = 8

Number of children is 8

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2 years ago

Use the Euclidean Algorithm to compute the greatest common divisors indicated. (a) gcd(20, 12) (b) gcd(100, 36) (c) gcd(207, 496

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Answer:

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Step-by-step explanation:

The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.

The Euclidean algorithm solves the problem:

<em> Given integers </em> $a, b$ <em>, find </em> $d=gcd(a,b)$ <em />

Here is an outline of the steps:

Let $a=x$ , $b=y$ .
Given $x, y$ , use the division algorithm to write $x=yq+r$ .
If $r=0$ , stop and output $y$ ; this is the gcd of $a, b$ .
If $r\neq 0$ , replace $(x,y)$ by $(y,r)$ . Go to step 2.

The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.

Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:

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Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.

(a) To find $gcd(20, 12)$ we apply the Euclidean algorithm:

$20 = 12\cdot 1 + 8\\ 12 = 8\cdot 1 + 4\\ 8 = 4\cdot 2 + 0$

The process stops since we reached 0, and we obtain $gcd(20, 12)=4$ .

(b) To find $gcd(100, 36)$ we apply the Euclidean algorithm:

$100 = 36\cdot 2 + 28\\ 36 = 28\cdot1 + 8\\ 28 = 8\cdot 3 + 4\\ 8 = 4\cdot 2 + 0$

The process stops since we reached 0, and we obtain $gcd(100, 36)=4$ .

(c) To find $gcd(496,207 )$ we apply the Euclidean algorithm:

$496 = 207\cdot 2 + 82\\ 207 = 82\cdot 2 + 43\\ 82 = 43\cdot 1 + 39\\ 43 = 39\cdot 1 + 4\\ 39 = 4\cdot 9 + 3\\ 4 = 3\cdot 1 + 1\\ 3 = 1\cdot 3 + 0$

The process stops since we reached 0, and we obtain $gcd(496,207 )=1$ .

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3 years ago