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4 September, 01:17

A larger number is five more than twice a smaller number. Their sum is 80. Find the numbers.

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Answers (2)
  1. 4 September, 01:39
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    The smaller number is 25 and the larger number is 55.

    Step-by-step explanation:

    1. Let's call the larger number a and the smaller number b.

    2. If the larger number is five more ( + 5) than twice (*2) the smaller number, we can write this as:

    a = 2b + 5

    3. Given that the sum of the larger and smaller number is 80, we can also write the following equation:

    a + b = 80

    4. We now have two equations:

    (1) a = 2b + 5

    (2) a + b = 80

    Our aim is to now find the values of a and b. There are many different ways to continue from here, however since the first equation is already in terms of a, I would personally substitute this into the second equation:

    given that a = 2b + 5:

    a + b = 80

    2b + 5 + b = 80 (Substitute a for 2b + 5)

    3b + 5 = 80 (Add 2b and b)

    3b = 75 (Subtract 5 from both sides)

    b = 25 (Divide both sides by 3)

    5. Now, given that b = 25, we can substitute this into equation (1) to get:

    a = 2b + 5

    a = 2 (25) + 5

    a = 50 + 5

    a = 55

    6. Thus, the smaller number is 25 and the larger number is 55.
  2. 4 September, 01:44
    0
    The first number is 25. The larger number is 55

    Step-by-step explanation:

    There was a lot of trial and error but it works. 25*2=50

    50+5=55

    55+25=80
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