Answer:
50 & 105
Step-by-step explanation:
We need to find the 2 numbers >>>>
Let first number be a
and second number be b
Also, let a < b
Now, "twice a number PLUS twice another number is 310". Thus, we can write an equation as:
2a + 2b = 310
The difference (larger minus smaller) is 55, so we can write:
b - a = 55
also can be written as b = 55 + a
Now we replace 1st equation with 2nd equation and write an equation in "a" and solve for a first:
[tex]2a + 2b = 310\\2a + 2(55+a) = 310\\2a + 110 + 2a = 310\\4a + 110 = 310\\4a = 310 - 110\\4a = 200\\a=50[/tex]
We know,
b = 55 + a
so
b = 55 + 50
b = 105
So the two numbers are 50 & 105
