QuestionTrei numere naturale $a, b, c$ : $b = 2a + 3$ , $c = 4a$ . Află procentul lui $a$ din $c$ și numerele, suma fiind 87.

Studdy Solution

STEP 1

Assumptions1. $a, b, c$ are non-zero natural numbers. $a$ is different from $03.$ b $divided by$ a $gives a quotient of and a remainder of34.$ c $is4 times larger than$ a $<br />5. The sum of$ a, b, c$ is87

STEP 2

First, let's express $b$ in terms of $a$ using the division remainder theorem, which states that for any integers $a$ and $b$ , there exist unique integers $q$ and $r$ such that $b = aq + r$ .
$b =2a +$

STEP 3

Next, let's express $c$ in terms of $a$ using the given condition that $c$ is times larger than $a$ .
$c =a$

STEP 4

Now, let's express the sum of $a, b, c$ in terms of $a$ using the given condition that their sum is87.
$a + b + c =87$

STEP 5

Substitute $b$ and $c$ from steps2 and3 into the equation from step4.
$a + (2a +3) + (4a) =87$

STEP 6

implify the equation to find the value of $a$ .
$a +3 =87$

STEP 7

Subtract3 from both sides of the equation to isolate $7a$ .
$7a =87 -3$

STEP 8

Calculate the right side of the equation.
$7a =84$

STEP 9

Divide both sides of the equation by7 to solve for $a$ .
$a =84 /7$

STEP 10

Calculate the value of $a$ .
$a =12$

STEP 11

Substitute $a =$ into the equations from steps and3 to find the values of $b$ and $c$ .
$b =() +3$ $c =4()$

STEP 12

Calculate the values of $b$ and $c$ .
$b =27$ $c =48$ The three numbers are $a =12, b =27, c =48$ .

STEP 13

To find out what percentage of $c$ is represented by $a$ , we use the formula for percentage $Percentage = (a / c) \\times100\%$

STEP 14

Substitute $a =12$ and $c =48$ into the formula.
$Percentage = (12 /48) \\times100\%$

STEP 15

Calculate the percentage.
$Percentage =25\%$ So, $a$ represents25% of $c$ .

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