a personal trainer designs exercise plans based on a combination of strength - training and aerobic…

a personal trainer designs exercise plans based on a combination of strength - training and aerobic exercise. a beginner plan has 15 minutes per session of strength - training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. an advanced plan has 20 minutes per session of strength - training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week. which statement describes when the plans are based on the same number of aerobic exercise sessions? each plan utilizes a combination of 2 strength - training sessions and 2 aerobic exercise sessions per week. each plan utilizes a combination of 2 strength - training sessions and 3 aerobic exercise sessions per week. each plan utilizes a combination of 3 strength - training sessions and 2 aerobic exercise sessions per week. each plan utilizes a combination of 3 strength - training sessions and 3 aerobic exercise sessions per week.

a personal trainer designs exercise plans based on a combination of strength - training and aerobic exercise. a beginner plan has 15 minutes per session of strength - training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. an advanced plan has 20 minutes per session of strength - training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week. which statement describes when the plans are based on the same number of aerobic exercise sessions? each plan utilizes a combination of 2 strength - training sessions and 2 aerobic exercise sessions per week. each plan utilizes a combination of 2 strength - training sessions and 3 aerobic exercise sessions per week. each plan utilizes a combination of 3 strength - training sessions and 2 aerobic exercise sessions per week. each plan utilizes a combination of 3 strength - training sessions and 3 aerobic exercise sessions per week.

Answer

Explanation:

Step1: Set up equations

Let $x$ be the number of strength - training sessions and $y$ be the number of aerobic exercise sessions. For the beginner plan, the equation is $15x + 20y=90$. For the advanced plan, the equation is $20x + 30y = 130$.

Step2: Simplify the beginner - plan equation

Divide the equation $15x + 20y=90$ by 5, we get $3x + 4y = 18$, then $y=\frac{18 - 3x}{4}$.

Step3: Simplify the advanced - plan equation

Divide the equation $20x+30y = 130$ by 10, we get $2x + 3y=13$, then $y=\frac{13 - 2x}{3}$.

Step4: Equate the two expressions for $y$

$\frac{18 - 3x}{4}=\frac{13 - 2x}{3}$. Cross - multiply: $3(18 - 3x)=4(13 - 2x)$.

Step5: Expand and solve for $x$

$54-9x = 52 - 8x$. Add $9x$ to both sides: $54=52 - 8x+9x$. So $x = 2$.

Step6: Substitute $x = 2$ into one of the $y$ expressions

Substitute $x = 2$ into $y=\frac{18 - 3x}{4}$, we have $y=\frac{18-3\times2}{4}=\frac{18 - 6}{4}=3$.

Answer:

Each plan utilizes a combination of 2 strength - training sessions and 3 aerobic exercise sessions per week.