Three times a number increased by five times another number is 49, but twice the second number exceeds five times the first numb

Question

Makovka662

10 days ago

15

Three times a number increased by five times another number is 49, but twice the second number exceeds five times the first numb

er by 1. What are the numbers?

Spanish

2 answers:

sleet_krkn [1.1K] · Answer 1 · 2026-03-26T06:44:27+03:00

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Let x = "a number"

Let y = "another number"

:

Create an equation for each statement:

:

"three times a number increased by five times another number is 49"

3x + 5y = 49

:

"twice the second number exceeds five times the first number by 1."

2y = 5x + 1

In rewritten standard form

-5x + 2y = 1

:

what are the numbers?

:

Multiply the 1st equation by 5, and the 2nd equation by 3

15x + 25y = 245

-15x + 6y = 3

---------------Adding to eliminate x; find y:

0x + 31y = 248

$y = \frac{248}{31}$

y = 8

:

Determine x using the first equation

3x + 5(8) = 49

3x = 49 - 40

$x = \frac{9}{3}$

x = 3

Verify solutions in the second equation:

2(8) = 5(3) + 1

16 = 15 + 1; confirms our solution

ɪ ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘꜱ❤

Novay_Z [1K] · Answer 2 · 2026-03-26T06:45:25+03:00

Answer:

3 and 8

Explanation:

3a + 5b = 49

2b = 5a + 1

thus:

2b - 5a = 1 equation 1

-5a + 2b = 1 equation 2

therefore:

multiplying equation 2 by -2.5 and adding to equation 1:

3a + 5b = 49

12.5a - 5b = -2.5

15.5a + 0 = 46.5

15.5a = 46.5

a = 46.5/15.5

a = 3

2b = 5a + 1

2b = (5*3) + 1

2b = 15 + 1

2b = 16

b = 16/2

b = 8

Verification:

3a + 5b = 49

3*3 + 5*8 = 49

9 + 40 = 49