Increasing/Decreasing by a Percent - 9
The smaller number is 4 and the larger is 11 – x == 11 – 4 = 7.
Algebra students are often asked to compute people’s ages. The steps I solving such problems are usually the same as those used above.
The smaller number is 4 and the larger is 11 – x == 11 – 4 = 7.
Algebra students are often asked to compute people’s ages. The steps I solving such problems are usually the same as those used above.
Alfi Blog Maret 14, 2026 Admin Bandung IndonesiaExamples
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.
Alfi Blog Maret 13, 2026 Admin Bandung IndonesiaIncreasing/Decreasing by a Percent - 8
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.
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.
Alfi Blog Maret 12, 2026 Admin Bandung IndonesiaIncreasing/Decreasing by a Percent - 7
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.
Examples
The sum of
two numbers is 70. One number is eight more than the other. What are the two
numbers?
Problems such as this are similar to the above in that we are looking for two or more numbers and we have a little information about how far apart the numbers are. In the problems above, the numbers differed by one. Here, two numbers differ by eight.
Alfi Blog Maret 11, 2026 Admin Bandung IndonesiaIncreasing/Decreasing by a Percent - 6
Examples
The sum of
two numbers is 70. One number is eight more than the other. What are the two
numbers?
Problems such as this are similar to the above in that we are looking for two or more numbers and we have a little information about how far apart the numbers are. In the problems above, the numbers differed by one. Here, two numbers differ by eight.
Many problems require the student to use common sense to solve them—that is, mathematical reasoning. For instance, when a problem refers to consecutive integers, the student is expected to realize that any two consecutive integers differ by one. If two numbers are consecutive, normally x is set equal to the first and x + 1, the second.
Alfi Blog Maret 10, 2026 Admin Bandung IndonesiaIncreasing/Decreasing by a Percent - 5
Many problems require the student to use common sense to solve them—that is, mathematical reasoning. For instance, when a problem refers to consecutive integers, the student is expected to realize that any two consecutive integers differ by one. If two numbers are consecutive, normally x is set equal to the first and x + 1, the second.
