Chapter 8 linear appliCaTionS 247PRACTICE- The sum of two numbers is 10. Three times the smaller plus five times
the larger number is 42. What are the numbers? - The difference between two numbers is 12. Twice the smaller plus four
times the larger is 108. What are the two numbers? - The difference between two numbers is 8. The sum of one and a half times
the smaller and four times the larger is 54. What are the numbers? - The sum of two numbers is 11. When twice the larger is subtracted from
five times the smaller, the difference is 6. What are the numbers?
✔SOLUTIONS
- Let x represent the smaller number. The larger number is then 10 − x.
3510 42
3505 42
25042
50 50
28
xx
xx
xx
x+−=
+−=
−+=
−−
−=−
=()−−
−
=8
2
x 4
The numbers are 4 and 10 – x = 10 – 4 = 6.- The difference between the numbers is 12, so one number is 12 more
than the other. Let x represent the smaller number. Then x+ 12 is the
larger. Twice the smaller is 2x, and four times the larger is 4(x + 12).
2412 108
2448 108
648 108
48 48
660xx
xx
xx
x++=
++=
+=
−−
=()==
=60
6
x 10
The smaller number is 10 and the larger is x + 12 = 10 + 12 = 22.- The difference between the numbers is 8, so one of the numbers is 8
more than the other. Let x represent smaller number. The larger number
PRACTICE- The sum of two numbers is 10. Three times the smaller plus five times