Question

Students in Miss Moseley's fourth grade class are learning multiplication, and they demonstrate mastery by passing assessments. Travis has passed 11 tests, and his classmate, Jenifer, has passed 2 tests. Going forward, Travis plans to pass 2 tests per week. Meanwhile, Jenifer plans to pass 5 tests per week. Eventually Jenifer will catch up to Travis. When the number of tests each student has passed are equal, how many tests will each student have passed and how many weeks will it take?

Answer 1

Answer:

Each will pass 17 test after 3 weeks.

Step-by-step explanation:

Consider the provided information,

Let x is the number of weeks.

Travis has passed 11 tests and plans to pass 2 tests per week.

$11+2x$

Jenifer, has passed 2 tests and plans to pass 5 tests per week.

$2+5x$

Now equate them as shown.

$11+2x=2+5x$

$11-2=5x-2x$

$9=3x$

$x=3$

Hence, after 3 weeks both have passed the same number of test.

Substitute x=3 in $11+2x$

$11+2(3)=17$

Hence, each will pass 17 test after 3 weeks.

Answer 2

Answer:
Each will have passed 17 tests and it will take 3 weeks.

Explanation:
Let x be the number of weeks.
The number of tests Travis passes to begin with is 11.
We then add 2 tests per week, or 2x to that, giving us:
11+2x.

The number of tests Jenifer has passed to begin with is 2.
We then add 5 tests per week, or 5x to that, giving us:
2+5x.

Setting these equal, we have:
11+2x=2+5x.

Subtract 2x from each side:
11+2x-2x=2+5x-2x;
11=2+3x.

Subtract 2 from each side:
11-2=2+3x-2;
9=3x.

Divide both sides by 3:
$\frac{9}{3} = \frac{3x}{3}$;
3=x.

It will take 3 weeks.
In 3 weeks,
Travis will have passed:
11+2*3 = 11+6 = 17 tests.
Jenifer will have passed the same number, since she catches up with him at this point.