Examples
The
difference between two numbers is 13. Twice the smaller plus three times the
larger is 129.
If the difference between two numbers is 13, then one of the numbers is 13 more than the other. The statement ‘‘The difference between two numbers is 13,’’ could have been given as, ‘‘One number is 13 more than the other.’’ As before, let x represent the first number. Then, x + 13 represents the other. ‘‘Twice the smaller’’ means ‘‘2x’’ (x is the smaller quantity because the other quantity is 13 more than x). Three times the larger number is 3(x + 13). ‘‘Twice the smaller plus three times the larger is 129’’ becomes 2x + 3(x + 13) = 129.
The numbers
are 18 and x + 13 = 18 + 13 = 31.
The sum of
two numbers is 14. Three times the smaller plus twice the larger is 33. What
are the two numbers?
Let x represent the smaller number. How can
we represent the larger number? We know that the sum of the smaller number and
larger number is 14. Let ‘‘?’’ represent the larger number and we’ll get ‘‘?’’ in
terms of x.
The smaller number plus the larger number is
14.
So, 14 – x
is the larger number. Three times the smaller is 3x. Twice the larger is 2(14 –
x). Their sum is 33, so 3x + 2(14 – x) = 33.
The smaller
number is 5 and the larger is 14 – x = 14 – 5 = 9.
Practice
1.
The sum of two numbers is 10. Three times the
smaller plus 5 times the larger number is 42. What are the numbers?
2.
The difference between two numbers is 12. Twice
the smaller plus four times the larger is 108. What are the two numbers?
3.
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?
4.
The sum of two numbers is 11. When twice the
larger is subtracted from 5 times the smaller, the difference is 6. What are
the numbers?
Solutions
1. Let
x represent the smaller number. The larger number is then 10 – x.
The
numbers are 4 and 10 – x = 10 – 4 = 6.
2. 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).
The
smaller number is 10 and the larger is x + 12 = 10 + 12 = 22.
3. 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 is x þ 8. One and a
half of the smaller number is 1 ½ x, four times the larger is 4(x + 8).
The
smaller number is 4 and the larger, x + 8 = 4 + 8 = 12.
4. Let
x = smaller number. Then 11 – x is the larger. Five times the smaller is 5x,
and twice the larger is 2(11 – x). ‘‘Twice the larger subtracted from 5 times
the smaller’’ becomes ‘‘5x – 2(11 – x).’’
The
smaller number is 4 and the larger is 11 – x = 11 – 4 = 7.
“Sumber Informasi”
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