Vogt’s “Beginning Word
Problems (One Unknown Variable)”
1.
When twice an unknown number is added to thirteen, the sum is twenty-five.
2.
When twenty-five is added to three times an unknown number, the sum is
thirty-four.
3.
Five times an unknown number decreased by eight is twenty-two.
4.
Four times an unknown number decreased by five is fifteen.
5.
Twice an unknown number is equal to the sum of five and the unknown number.
6.
When seven is added to an unknown number, the result is twice that unknown
number.
7.
Seven minus an unknown number results in the same as one more than the unknown
number.
8.
Six plus an unknown number is equal to twelve decreased by the unknown number.
9.
When twice an unknown number is subtracted from fifteen, the result is the unknown
number.
10.
When three times an unknown number is subtracted from twenty, the result is the
unknown number.
11.
One-fifth of an unknown number is four.
12.
An unknown number divided by twelve equals six.
13.
When five is subtracted from one-third of an unknown number, the result is
four.
14.
When four is subtracted from one-half of an unknown number the result is six.
15.When an unknown number is subtracted from twelve the
difference is half of the number.
16.When a number is decreased by five, the difference is half
the number.
17.
Twice the sum of five and an unknown number is equal to twenty-six.
18.
Four times the sum of nine and an unknown number is equal to twenty.
19. When the sum of an
unknown number and itself is multiplied by three, the result is twenty-four.
20.
Five times the sum of an unknown number and itself is forty.
21.
Twice the result of subtracting an unknown number from five is eight.
22.
Three times the result of subtracting an unknown number from eight is twelve.
23. When twice the sum of
four and an unknown number is added to the unknown number, the result is the
same as when ten is added to the unknown number.
24. When six is subtracted
from five times an unknown number, the result is the same as when four is added
to three times the unknown number.
25. Three times the sum of
four and twice an unknown number is equal to four times the sum of three times
the unknown number and nine.
26. Five times the sum of
four and six times an unknown number is equal to four times the sum of twice
the unknown number and ten.
27.If
the sum of an unknown number and twelve is subtracted from four times the
unknown number, the result is the unknown number less four.
28. If twice an unknown
number is subtracted from the sum of six and the unknown number, the result is
the same as when five times the unknown number is subtracted from two.
Answers (nb The correct translation for #1 is 13 + 2n = 25 even though
the commutative property assures the same solution if it is translated to 2n + 13 = 25
):
1) {6} 2) {3} 3) {6} 4)
{5} 5) {5} 6) {7} 7) {3} 8) {3} 9)
{5}
10) {5} 11) {20} 12)
{72} 13) {27} 14) {20} 15) {8} 16) {10} 17)
{8} 18) {-4}
19) {4} 20) {4} 21)
{1} 22) {4} 23) {1} 24) {5} 25) {-4} 26)
{10/11} 27) {4} 28) {-1}
2) 3n + 25 = 34 4) 4n – 5 = 15 6) 4 + 7 = 2n 8)
6 + n = 12 – n 10) 20 – 3n = n
12) n/12
= 6 14) ˝ n – 4 = 6 16) n – 5 = ˝ n 18) 4(9 + n) = 20 20) 5(n + n) = 40
*
Vogt Educational Materials
22)
3(8 – n) = 12 24) 5n – 6 = 3n + 4 26) 5(4
+ 6n)
= 4(2n
+ 10) 28) (6 + n) – 2n = 2 – 5n
