Mathematics, 31.10.2020 21:10, sara12340

PLEASE HELP URGENT The sum of 3 numbers is 145. Seven times the second number is twice the first number and twice the second number is six times the third number.

Write the new ratio of the three numbers if the second number doubles and the third number is increased by one less than one fifth of the first number.

Answers: 1

Show answers

Answers

answered: kyleigh85

7:4:2

Step-by-step explanation:

Assign variables for the 3 numbers. Let the first number be x, the second number be y, and the third number be z.

"The sum of the 3 numbers is 145", therefore:

$\text{Equation I}$

"Seven times the second number is twice the first number":

$\text{Equation II}$

"Twice the second number is six times the third number":

$\text{Equation III}$

We can solve for x, y and z using this system of equations. Let's solve for y in the first equation by putting the other variables in terms of y in Equations II and III.

Solve for x in $\text{Equation II}$ :

$x=\frac{7}{2}y$

Solve for z in $\text{Equation III}$ :

$z=\frac{2}{6} y= \frac{1}{3} y$

Substitute these values into $\text{Equation I}$ to solve for y.

$\frac{7}{2} y+y+\frac{1}{3} y=145$

Combine like terms using common denominators. The least common denominator is 6. Multiply $\frac{7}{2} y$ by $\frac{3}{3}$ , multiply by $\frac{6}{6}$ , and multiply $\frac{1}{3} y$ by $\frac{2}{2}$ to make all of the denominators = 6.

$(\frac{3}{3})\frac{7}{2} y +(\frac{6}{6})y+(\frac{2}{2})\frac{1}{3} y=145$ $\frac{21}{6}y + \frac{6}{6}y + \frac{2}{6}y=145$

Add the fractions together.

$\frac{29}{6}y=145$

Solve for y by multiplying both sides by $\frac{6}{29}$ .

$y=145(\frac{6}{29} )= \frac{870}{29} =30$

We have found that y = 30. Now we can use this known value in order to solve for both x and z in Equations II and III.

$\text{Equation II}:$

$\text{Equation III}:$

We have found that x = 105, y = 30, and z = 10. Now we can write the new ratio of these 3 numbers:

"Write the new ratio of the three numbers if the second number doubles and the third number is increased by one less than one fifth of the first number":

$z+ (\frac{1}{5} x-1)$

The question asks for the new ratio once we evaluate these expressions. The variable x is the only one that stays the same at the end: 105.

$(10)+[\frac{1}{5} (105)-1 ]\\ (10) + (21-1 )\\ (10)+(20)=30$

Our final numbers are x = 105, y = 60, and z = 30. We can create the ratio between these numbers by fully simplifying them. Right now we have x:y:z=105:60:30 . Start by dividing all of the numbers by 5.

We get 21:12:6 . This ratio can be simplified further by dividing all of the numbers by 3. We then get the ratio of: 7:4:2 .

This ratio cannot be simplified any further, therefore, it is the new ratio of the three numbers.

answered: Guest

This is what i found “answer: a rigid transformation preserves both the side lengths and the angle measures of a polygon. step-by-step explanation: rigid transformations are the transformations which does not affect the size and the shape of figure .” i hope this you for what your looking for. can you plz mark me brainliest?

answered: Guest

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 13:40, HomeWorkForLife

The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to the temperature of the gas. if the pressure is 6 pounds per square inch when the temperature is find the pressure exerted when the temperature of the gas is 380 degrees f show work for the

Answers: 2

continue

Mathematics, 21.06.2019 19:00, breannaasmith1122

Which of the expressions (on the photo document i inserted) together represent all solutions to the following equation? 8cos(12x)+4=-4 *the answer should be in degrees.* > i would like for someone to explain the process to find the solutions for this.

Answers: 2

continue

Mathematics, 21.06.2019 21:30, Officaljazz18

Which best describes the construction of a triangle if given the segment lengths of 2 cm, 3 cm, and 5 cm? a) unique triangle b) cannot be determined c) triangle not possible d) more than one triangle

Answers: 1

continue

Mathematics, 22.06.2019 01:30, koiryrubio

Sandy is upgrading her internet service. fast internet charges $20 for installation and $52.45 per month. quick internet has free installation but charges $57.45 per month. part 1 out of 2 complete the equation that can be used to find the number of months after which the internet service would cost the same. use the variable x to represent the number of months of internet service purchased.

Answers: 1

continue

Do you know the correct answer?

PLEASE HELP URGENT The sum of 3 numbers is 145. Seven times the second number is twice the first nu...