Question

1. eleana and her grandfather both had birthdays last week.

• the sum of their ages is 100 years.
• her grandfather’s age is 4 times eleana’s age.

how old is eleana?
a. 16 years b. 20 years
c. 22 years d. 25 years

1. use the space below to complete the following question(s).

a car rental company has 2 rental plans. plan a charges $49.00 per day. plan b charges $25.00 per day, plus $0.10 per mile. how many miles must teri drive in one day for plan a to cost the same as plan b?

1. given:

$6x - 3y = 42$
$4x + 2y = -4$
what is $x + y$?
a. -6 b. -5 c. 4 d. 9

1. a system of equations is shown below.

$y = 3x - 1$
$y = -2x + 4$
what is the sum of $x$ and $y$ in the solution to the system?
a. 2 b. 3 c. 4

Explanation:

Question 20

Step1: Define variables

Let $E$ = Eleana's age, $G$ = Grandfather's age.

Step2: Set up equations

$E + G = 100$, $G = 4E$

Step3: Substitute and solve

Substitute $G=4E$ into first equation:
$E + 4E = 100$
$5E = 100$
$E = \frac{100}{5} = 20$

Step1: Define variables and costs

Let $m$ = number of miles. Cost of Plan A: $\$49.00$, Cost of Plan B: $25 + 0.10m$

Step2: Set costs equal

$49 = 25 + 0.10m$

Step3: Solve for m

$0.10m = 49 - 25$
$0.10m = 24$
$m = \frac{24}{0.10} = 240$

Step1: Eliminate y from equations

Multiply first equation by 2: $12x - 6y = 84$
Multiply second equation by 3: $12x + 6y = -12$

Step2: Add equations to solve x

$12x - 6y + 12x + 6y = 84 + (-12)$
$24x = 72$
$x = \frac{72}{24} = 3$

Step3: Substitute x to find y

Use $4x + 2y = -4$:
$4(3) + 2y = -4$
$12 + 2y = -4$
$2y = -16$
$y = -8$

Step4: Calculate x+y

$x + y = 3 + (-8) = -5$

Answer:

B. 20 years

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Question 21