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A. In 1 year Kristen will be four times as old as Danielle. Ten years from then Kristen will only be twice as old as Danielle. How old is Kristen now?


B. The greater of two integers is 4 times the lesser. Of the lesser integer is increased by 12, the result is 3 less than the greater.Find the integers.

C. One number exceeds another by 12, and the sum of the smaller number and twice the larger number is 93. Find the numbers.

  • math -

    Let present age of Kristen be x and of Daniel be y.Then after 1 year,
    x+1=4(y+1)or x-4y=3.....Eq.1
    After 10 yrs from then, ages will be
    (x+1)+10=2[(y+1)+10] Or x+11=2y+22
    Or x-2y=11 .....Eq.2. Subtract eq. 1 from eq.2 and solve. We get y=4 and x=19.
    Check: After 1 year Kristen will be 20 and Daneil will be 5. After another 10 yrs K will be 30 and D will be 15. OK.

    Let smaller and greater integers be x and 4x. Then x+12=4x-3 or -3x=-15
    Or x=5, and larger integer will be 20.
    Check: 5+12=17=20-3. OK.

    Let smaller no. be x, so larger one is x+12. Now x+2(x+12)=93
    Or x+2x+24=93 or 3x=93-24=69
    Hence x=69/3=23 and larger no. is 23+12=35. Check:23+35*2=23+70=93, OK.

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