Mathematics, 20.12.2019 02:31 griffinalexis2780

In 10 minutes, courtney can write out four christmas cards. in the same time, victoria can write 14 christmas cards. if they work together, how long will it take them to write out 252 christmas cards?

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Answer from: bobduncan1086

To write 252 cards together Courtney and Victoria will take = 140 minutes or 2 hours and 20 minutes.

Step-by-step explanation:

Given:

Courtney writes 4 cards in 10 minutes

Victoria writes 14 cards in 10 minutes.

To find the time taken by them to write 252 cards working together.

Solution:

Using unitary method to determine their 1 minute work.

In 10 minutes Courtney writes = 4 cards

So,in 1 minute Courtney will write = $\frac{4}{10}$ cards

In 10 minutes Victoria writes = 14 cards

So,in 1 minute Victoria will write = $\frac{14}{10}$ cards

Now, Courtney and Victoria are working together.

So, in 1 minute, number of cards they can write together will be given as:

⇒ $\frac{4}{10}+\frac{14}{10}$

Since we have common denominators, so we can simply add the numerators.

⇒ $\frac{18}{10}$

Again using unitary method to determine the time taken by them working together to write 252 cards.

They can write $\frac{18}{10}$ cards in 1 minute.

To write 1 card they will take = $\frac{1}{\frac{18}{10}}=\frac{10}{18}$ minutes

So, for 252 cards the will take = $\frac{10}{18}\times252=\frac{2520}{18}=140$ minutes

140 minutes = (60+60+20) minutes = 2 hours and 20 minutes [ As 60 minutes = 1 hour]

So, to write 252 cards together Courtney and Victoria will take = 140 minutes or 2 hours and 20 minutes.

Answer from: Quest

step-by-step explanation:

the answer would be 7

Answer from: Quest

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = $\frac{-8+3}{4-7}$ = - $\frac{5}{3}$

y = - $\frac{5}{3}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - $\frac{20}{3}$ + c ⇒ c = - $\frac{4}{3}$

y = - $\frac{5}{3}$ x - $\frac{4}{3}$ ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

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