Question

1. for the past three months, grace used her cell phone for 43 minutes, 62 minutes, and 57 minutes. how many minutes would she have to use her cell phone this month for the average usage over the four months to be 55 minutes? 10. a triangle has one angle measuring 3x degrees. a second angle measures (2x + 20) degrees and the third angle measures (4x - 20) degrees. what is the value of x? 11. you and a friend buy two fruit smoothies and leave a tip. you split the total and your half comes to $3.60. what percent tip (in decimal form) did you and your friend leave if the fruit smoothies cost $3 each?

Explanation:

9.

Step1: Recall average formula

The average of a set of numbers is $\frac{\text{Sum of numbers}}{\text{Number of numbers}}$. Let the number of minutes used this month be $x$. The sum of minutes for 4 months is $43 + 62+57 + x$, and the number of months is 4, and the average is 55. So we have the equation $\frac{43 + 62+57 + x}{4}=55$.

Step2: Simplify the sum in the numerator

$43+62 + 57=162$. The equation becomes $\frac{162 + x}{4}=55$.

Step3: Solve for $x$

Multiply both sides of the equation by 4: $162 + x=55\times4 = 220$. Then subtract 162 from both sides: $x=220 - 162=58$.

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180 degrees. So we set up the equation $3x+(2x + 20)+(4x-20)=180$.

Step2: Combine like - terms

Combining the $x$ terms: $3x+2x + 4x=9x$, and combining the constant terms: $20-20 = 0$. The equation simplifies to $9x=180$.

Step3: Solve for $x$

Divide both sides of the equation by 9: $x=\frac{180}{9}=20$.

Step1: Calculate the cost of smoothies

The cost of two fruit smoothies is $2\times3=\$6$.

Step2: Calculate the total amount paid

Since your half of the total (including tip) is $\$3.60$, the total amount paid is $2\times3.60=\$7.20$.

Step3: Calculate the tip amount

The tip amount is the total amount paid minus the cost of smoothies, so $7.20 - 6=\$1.20$.

Step4: Calculate the tip percentage

The tip percentage (in decimal form) is $\frac{\text{Tip amount}}{\text{Cost of smoothies}}=\frac{1.20}{6}=0.2$.

Answer:

58

10.