Can you decipher the quotation?

We have two conditions for the tokens Riley and Erik have earned. Let's call x and y to the number of tokens of Riley and Erik respectively. The first condition states that

$x+y=135$

Solving for y

$y=135-x$

The second condition is that the ratio of the number of tokens that Riley had to the number of tokens that Erik has is 8 to 7. It's written as

$\displaystyle \frac{x}{y}=\frac{8}{7}$

Or equivalently

$7x=8y$

Replacing y from the first equation

$7x=8(135-x)$

Operating

$7x=1080-8x$

Simplifying

$15x=1080$

$\boxed{x=72}$

Riley has 72 tokens

3 0

3 years ago

Twice the product of 3and a number exceeds the sum of the number and 80 by 10.what is the number?

Hatshy [7]

First, create an equation with the criteria given.

If we let x be your number,
$2(3x) = 80 + x + 10$
( $2(3x)$ is twice the product of 3 and x, and if it exceeds $x+80$ by 10, then we add 10 to $x+80$ to make the two sides of the equation equal.)

Now, solve for $x$ .

$6x=90+x \\ 5x=90 \\ x=18$

6 0

3 years ago

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.

8 0

3 years ago