Math

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1. What is the largest integer that is a factor of all three of the following numbers: 2160, 1344, 1440?

a) 6 b) 8 c) 12 d)16 e) none of these

2. The annual income of a family is budgeted as follows:

1/10 for clothing, 1/3 for food, and 1/5 for rent.

This leaves $1320 for other expenses and savings. Find the annual income.

a) $2156 b) $3600 c) $23,760
d) $39,600 e) none of these answers

  • Math -

    2160 = 2*2*2*2*3*3*3*5
    1344 = 2*2*2*2*2*2*3*7
    1440 = 2*2*2*2*2*3*3*5

    HCF = 2*2*2*2*3
    = 24

    2.
    let their income be x
    x/10 + x/3 + x/5 + 1320 = x
    times 150 , the LCM
    15x + 50x + 30x + 198000 = 150x
    198000 = 55x
    x = 3600

  • Math -

    1344 = 1*1344 = 1*2*672 = 1*2*3*224 =
    1*2*3*4*56 = 1*2*3*4*7*8.

    1440 = 1*1440 = 1*2*720 = 1*2*3*240 =
    1*2*3*4*60 = 1*2*3*4*5*12=1*2*3*4*5*6*2

    2160 = 1*2160 = 1*2*1080 = 1*2*3*360 =
    1*2*3*4*90 = 1*2*3*4*5*18=1*2*3*4*5*6*3

    GCF = 4.

    2. Income = $X.
    (1/10+1/3+1/5)X + 1320 = X
    (3/30+10/30*6/30)X + 1320 = x
    19x/30 + 1320 = x
    Multiply both sides by 30:
    19x + 39,600 = 30x
    -11x = -39,600
    X = $3600

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