Marsha has two numbers, $a$ and $b$. When she divides $a$ by 70 she gets a remainder of 64. When she divides $b$ by 105 she gets a remainder of 99. What remainder does she get when she divides $a+b$ by 35?

Remainder is 425

Step-by-step explanation:

Let the two numbers Marsha has be A & B

From the question, we have the first equation as

A : 70 = 64

Multiply both right and left sides by 70, we have:

A = 70 * 64 = 4,480

A = 4,480

From the question, we have the second equation as:

B : 105 = 99

Multiply both left and right sides by 105, we have:

B = 105 * 99 = 10,395

B = 10,395

Remainder = (A + B) : 35 = (4,480 + 10,395) : 35

Remainder = 14,875 : 35 = 425

Remainder = 425