Question

Andy and Jacob work as technicians in a laboratory where gemstones are tested and certified. Andy has already tested 30 gemstones and continues testing at a rate of 30 gemstones per hour. Jacob has already tested 40 gemstones and continues testing at a rate of 25 gemstones per hour.

Which function can Andy and Jacob use to determine the total number of gemstones they have tested after x hours? How many gemstones will they have tested after 5 hours?

A.
The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 60x + 65. Thus, they will have tested 365 gemstones in 5 hours.
B.
The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 70. Thus, they will have tested 345 gemstones in 5 hours.
C.
The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 70x + 55. Thus, they will have tested 405 gemstones in 5 hours.
D.
The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 10. Thus, they will have tested 285 gemstones in 5 hours.

Answer 1

B. This is true

The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 70. Thus, they will have tested 345 gemstones in 5 hours.

Explanation :

Andy tests 30 gemstones in 1 hour and Jacob tests 25 gemstones in 1 hour. Together they both test 30+25=55 gemstones in 1 hour

Let the given point of time be = x

so, 30x+25x=55x where x can be any given hour

So Andy has already tested 30 gemstones and Jacob has tested 40 gemstones so together they have tested 30+40=70

Hence, the function f(x)=55x+70 is true.

And when t = 5; then gems are 345.