If 5 times the smaller of 2 numbers is subtracted from twice the larger, the result is 16. if the larger is...

Question

(con't)...increased by 3 times the smaller, the result is 63. find the numbers.

Answer 1

Rewrite these word descriptions into mathematical equations. Denote a = smaller number and b = larger number. Then you can write the following equations using the descriptions above:

2b - 5a = 16 --------(1)
b + 3a = 63 --------(2)

Now solve for 'a' and 'b'. You can use whatever method to solve. I'll use the elimination method. Multiply (2) by -2 and add to (1)

-11a = -110 ----> a = 10

Now substitute in either (1) or (2). I'll substitute into (1)

2b - 5(10) = 16
2b = 66
b = 33

Also, make sure the following constraint is met, (b>a) = 33>10, which does hold. Thus

smaller # = 10
bigger # = 33

-------

Hope this helps

Answer 2

the two numbers are 10 and 33. this is how i got the answer.

i made X the smaller number and
Y the bigger number.

then, i deciphered the word problems above, and got two equations with two unknowns.

1) 2Y - 5X = 16
2) Y + 3X = 63

then, i multiplied the entire second equation by -2 (this way the Y terms will cancel out).

so i have:
1) 2Y - 5X = 16
2) -2Y - 6X = -126

now the y terms cancel out and you add up everything else:
-11X = - 110
and you calculate from this that X = 10

now that you have X you can go back to EITHER of the ORIGIONAL equations that you had, and plug in "10" for the value "X". after you do this you can easily solve for Y and find that Y = 33.

so the smaller number (X) = 10
and the bigger number (Y) = 33
done.

Answer 3

x : small y : large 2y -5x = 16 y + 3x = sixty 3 y = sixty 3-x replace: 2(sixty 3-3x)-5x = 16 126 - 6x -5x = 16 126 - 11x =16 100 and ten=11x x=10 plug x lower back into equation y = sixty 3-3x y= sixty 3 - 3(10) y = 33 more effective decision is an same as 33

Answer 4

33 and 10

Answer 5

2x - 5y = 16
x + 3y = 63

x + 3y = 63
x = -3y + 63

2(-3y + 63) - 5y = 16
-6y + 126 - 5y = 16
-11y = -110
y = 10

x = -3(10) + 63 = -30 + 63 = 33

ANS : 10 and 33

Answer 6

2x-5y=16
x+3y=63
2x+6y=126
2x-5y=16
11y=110
y=10
2x-50=16
2x=66
x=33