Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Students in Mrs. Schmidt's third grade class are working on times tables, and they demonstrate mastery by passing tests. Quincy has passed 8 tests so far. His classmate, Shivani, has passed 4 tests of them. From now on, Quincy plans to take and pass 1 test per week. Meanwhile, Shivani plans to do 5 per week. At some point, Quincy will catch up to Shivani. How long will it take? How many tests will each child have passed? In
weeks, the children will each have passed
tests.
In
weeks, the children will each have passed
tests.

Step-by-step explanation:

We know that:

Work:

Hence, it will take 1 week for both classmates to catch up with each other. Now, let's substitute the value of w into the first equation to find how many tests have each child passed.

Hence, each child has passed about 9 tests.

Hoped this helped.

6 spoons of sugar for every 21 cups of flour

step-by-step explanation:

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb