if 5 times the smaller of two numbers is..?

Question

if 5 times the smaller of two numbers is subtracted from twice the larger,the result is 16.if the larger is increased by 3times the smaller,the result is 63.find the larger number.

Answer 1

x = large number, y = small number

2x - 5y = 16 ... (1)
x + 3y = 63 ... (2)

Multiply (1) with 3 at both side
6x - 15y = 48 ... (3)

Multiply (2) with 5 at both side
5x + 15y = 315 ... (4)

Add (3) and (4)
11x = 363
x = 33 (large number)

Answer 2

enable s = smaller form l = bigger form ===================== s + l = 19 ==> Eq. a million 5s = 2l - 3 ==> Eq. 2 ================ s + l = 19 ===> Eq. a million s = 19 - l ===> Eq. 3 replace Eq. 3 to Eq. 2 5s = 2l - 3 ==> Eq. 2 5( 19 - l) = 2l - 3 ninety 5 - 5l = 2l - 3 Transposition ninety 5 - ninety 5 - 5l - 2l = 2l - 2l - 3 - ninety 5 -7l = -ninety 8 l = -ninety 8/-7 l = 14 ===> bigger form replace the linked fee of l to Eq. a million s + l = 19 s + 14 = 19 s = 19 - 14 s = 5 ===> smaller form

Answer 3

x : small
y : large

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

y = 63-x
substitute:
2(63-3x)-5x = 16
126 - 6x -5x = 16
126 - 11x =16
110=11x
x=10

plug x back into equation
y = 63-3x
y= 63 - 3(10)
y = 33
larger number is equal to 33

Answer 4

L = larger
S = smaller
2L - 5S = 16
L + 3S = 63

L = 63 - 3S
2(63 - 3S) - 5S = 16
126 - 6S - 5S = 16
110 = 11S
10 = S
L + 3(10) = 63
L + 30 = 63
L = 33
check
2(33) - 5(10) = 16
66 - 50 = 16 checks