Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Band students are tested on, and required to pass, a certain number of scales during the year. As of today, Pablo has passed 15 scales, whereas his friend Kayla has passed 3 of them. Going forward, Pablo has committed to passing 1 scale per week, and Kayla has committed to passing 5 per week. At some point soon, the two friends will have passed the same number of scales. How long will that take? How many scales will that be?


In ? weeks, the friends will each have passed ? scales.

Answer 1

Answer:

The system of equation are $\left \{ {{15+1x} \atop {3+5x}} \right.$.

In 3 weeks, the friends will each have passed 18 scales.

Step-by-step explanation:

Let number of weeks be 'x'.

Given:

Number of scale Pablo has passed = 15 scales

Number of scale Kayla has passed = 3 scales

Number of scales passing per week by Pablo = 1 scale

Number of scales passing per week by Kayla = 5 scale

We need find the number of weeks when both have same scales.

First we will find the Total number of scales Pablo will passed after 'x' weeks.

Total number of scales Pablo will passed after 'x' weeks is equal to sum of Number of scale Pablo has passed and Number of scales passing per week by Pablo multiplied by number of weeks.

framing in equation form we get;

Total number of scales Pablo will passed after 'x' weeks = $15+1x$

Now we will find Total number of scales Kayla will passed after 'x' weeks.

Total number of scales Kayla will passed after 'x' weeks is equal to sum of Number of scale Kayla has passed and Number of scales passing per week by Kayla multiplied by number of weeks.

framing in equation form we get;

Total number of scales Kayla will passed after 'x' weeks = $3+5x$

Hence the system of equation are $\left \{ {{15+1x} \atop {3+5x}} \right.$.

Now we need to find the number of weeks when both have passed equal scales.

Hence we can say that;

Total number of scales Pablo will passed after 'x' weeks = Total number of scales Kayla will passed after 'x' weeks

Substituting the value we get;

$15+1x=3+5x$

On Solving the equation we get;

Combining like terms first;

$5x-x=15-3\\\\4x=12$

Now by Division property dividing both side by 4 we  get;

$\frac{4x}{4}=\frac{12}{4} \\\\x=3 \ weeks$

Now we will find the total scales passed by each after 3 weeks;

Total number of scales Pablo will passed after 3 weeks = $15+x=15+3 = 18 \ scales$

Total number of scales Kayla will passed after 3 weeks = $3+5x=3+5\times3 = 18 \ scales$

Hence: In 3 weeks, the friends will each have passed 18 scales.