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3 years ago

The difference between the two numbers is 48. The ratio of the two number is 7:3, what are the two numbers?

Mathematics

2 answers:

Arisa [49]3 years ago

7 0

Answer:

84 and 36

Step-by-step explanation:

The ratio of two numbers is 7:3.

We don't know what the numbers are, but since their ratio is 7:3, we can let the numbers be 7x and 3x. Notice that the ratio between 7x and 3x is 7x/3x = 7/3, so we still have the same ratio, 7:3.

The difference between the numbers is 48.

7x - 3x = 48

4x = 48

x = 12

7x = 7(12) = 84

3x = 3(12) = 36

The numbers are 84 and 36.

Check:

7/3 = 2.333...

84/36 = 2.333...

84 and 36 are int he same 7:3 ratio as 7:3.

84 - 36 = 48

The difference between 84 and 36 is 48 like the problem states.

This shows our answer, 84 and 36, is correct.

MAXImum [283]3 years ago

6 0

Hi, hope you’re having a good day today!!!

Answer:

84:36

(The explanation is really really long, so you may want to skip it, unless this is a test or you want a better understanding then, yeah)

So first, you have 7:3

Then, you have to multiply both by the same number to get an equal ratio to 7:3,

Let’s try 7*10=70 and 3*10=30 70-30=40, so you know that the answer is close,

Then, let’s try 7*11=77 and 3*11=33, subtract and you get 44. Nope, not the answer

So, finally let’s try 7*12=84 and 3*12=36, and 84-36=48!!!!

So, the answer is explained! Wait, but you still have to put them like ratios (if this chapter is ratios and proportions)

84:36 or 84 to 36, either way.

<h2>Have a great day!! ❤️❤️</h2>

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Erica earns $10.50 an hour for the first 40 hours. She is paid time and a half for every hour worked over 40 hours during a week

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Answer:

Step-by-step explanation:

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Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Li

Fittoniya [83]

Answer:

(a)

$r\geq 5$

$r+y\leq 15$

$8r+12y\geq 120$

$y\geq 0$

(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours

(d)Maximum Earning = $160

Step-by-step explanation:

Let r be the number of hours worked at the restaurant.

Let y be the number of hours of yard work,

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.

$r\geq 5$

Since she does yard work, $y\geq 0$

Lia’s parents allow her to work a maximum of 15 hours per week overall.

$r+y\leq 15$

Lia’s goal is to earn at least $120 per week.

The restaurant, r pays $8 per hour

Yard work, y pays $12 per hour.

Therefore:

$8r+12y\geq 120$

The system of inequalities that represent this problem is therefore:

$r\geq 5$

$r+y\leq 15$

$8r+12y\geq 120$

$y\geq 0$

(b)The graph of the inequality is attached below

(c)When the graph is plotted, the vertices of the feasible region are:

(5,10)
(5, 6.7)
(15,0)

Where the first term is for the number of hours worked in the restaurant.

The maximum value of r possible is 15 from the three points.

Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.

(d)Maximum Amount Lia can earn in 1 Week

At (5,10), Earning=(5X8)+(10X12)=40+120=$160

At (5, 6.7), Earning=(5X8)+(6.7X12)=40+80.4=$120.4
At (15,0) Earning=(15X8)+(0X12)=$120

Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.

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