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orwrite 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, luca has passed 9 scales, whereas his friend warren has passed 8 of them. going forward, luca has committed to passing 2 scales per week, and warren has committed to passing 3 per week. at some point soon, the two friends will have passed the same number of scales. how many scales will that be? how long will that take?

Respuesta :

After 1 week Luca and his friend  will have passed the same number of scales and the number of scales = 11

In this question, we have been given a situation.

we need to write a system of equations to describe the situation.

Let x be the number of weeks and y be the number scales.

luca has passed 9 scales, whereas his friend warren has passed 8 of them. going forward, luca has committed to passing 2 scales per week, and warren has committed to passing 3 per week.

So, we get a system of equations as:

y = 2x + 9

y =  3x + 8

We need to find the amount of time(weeks) it would take that the two friends will have passed the same number of scales.

Also, we need to find the number of scales.

When the two friends will have passed the same number of scales,

2x + 9 =  3x + 8

3x - 2x = 9 - 8

x = 1

After 1 week the two friends will have passed the same number of scales.

And  the number of scales would be,

y = 11

Therefore, after 1 week the two friends will have passed the same number of scales.

And  the number of scales would be 11

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