Question

The sum of two positive integers is 1287. If the larger number is 9.5 more than 2.5 times smaller number, then what are the two numbers?

Answer 1

Can you write an equation for the first statement "The sum of two positive integers is 1287." using x for one integer and y for the other?

Answer 2

It says the "sum" of the numbers... what arithmetic function is sum?

Answer 3

correct.

Now assume x is the larger number and y is the smaller number, can you write the equation for "the larger number is 9.5 more than 2.5 times smaller number"?

Answer 4

well, "2.5 times the smaller number" translates to?

Answer 5

great! Now if x is "9.5 more than" 2.5y?

Answer 6

Not quite. The equation for "the larger number is 9.5 more than 2.5 times smaller number" is given by x=9.5 ? 2.5y. what arithmetic function would be used for ? in that equation?

Answer 7

Hint: more than implies addition.

Answer 8

what arithmetic function is addition?

Answer 9

I dont understand what your asking.

Answer 10

Well, you got the first equation is
x+y=1287
The 2nd equation is x=9.5+2.5y (the larger number is 9.5 more than 2.5 times smaller number) substitute x back into the first equation and solve for y.

Answer 11

so i add 9.5 and 2.5? So 12y=x?

Answer 12

??

Answer 13

Solve the following for x and y:\[\left\{x+y=1287,x=\frac{25}{10}y+\frac{95}{10}\right\}\]

Answer 14

You can substitute x = 9.5 + 2.5y into x + y = 1287 so
(9.5 + 2.5y) + y = 1287
Solve for y