; 2 line pairs. Line @1 is the problem. Line @2 is the answer. Followed by a
; blank line.
;
; Numerical inputs are given by @letter, where letter is a..z.
;
; {xunknown} is replaced by "Let x be the unknown number."
;
; replace {dim} with selection of inches, m, cm, feet, yards...
;
; {name}=a list of names
;
; {whatevern}=n=1,2,3..a list of whatevers, given the name whatevern
;
; {findun}=The string "Find the unknown number."
;
; {long}=rope, cable, fabric, wire, string, yarn,
;
; {solvex}=Solve for x
;
; {trans}=Your word problem can be translated into this equation
;
; {another}=Another equation that can be written based on your problem is
;
; {intwarn}=Since the problem asks for <i>integers only</i>, fractions <b>are not</b> correct answers, even thought you may get a fraction as an answer (it just so happens that the numbers you chose for your problem give a fraction for an answer).
;
; {speed}=mph or km/hr
;
; {time}=hours, minutes, seconds, days
;
@a more than @b times an unknown number is @c. {findun}.
{xunknown}. @b times a number can be written like @bx, so {trans}: {@bx+@a=@c} {solvex} to get the unknown number.
@a times an unknown number, decreased by @b is @c. {findun}.
{xunknown}. @a times an unknown number can be written like @ax, so {trans}: {@ax-@b=@c} {solvex} to get the unknown number.
@a minus an unknown number is equal to the unknown number plus @b. {findun}.
{xunknown}. @a minus an known number is {@a-x} an unknwon number plus @b can be written like {@b+x} {trans}: {@a-x=x+@b} {solvex} to get the unknown number.
@a plus an unknown number is equal to @b decreased by the unknown number. {findun}.
{xunknown}. @a plus an unknown number is {@a+x} @b decreased by an unknown number is {@b-x} {trans}: {@a+x=@b-x} {solvex} to get the unknown number.
1/@a of an unknown number is @b. {findun}.
{xunknown}. 1/@a of an unknown number is x/@a. {trans}: {x/@a=@b} {solvex} to get the unknown number.
An unknown number divided by @a equals @b. {findun}.
{xunknown}. {trans}: {x/@a=@b} {solvex} to get the unknown number.
When @a is subtracted from 1/@b of an unknown number, the result is @c. {findun}.
{xunknown}. {trans}: {x/@b-@a=@c} {solvex} to get the unknown number.
@a times the sum of @b and an unknown number is equal to @c. {findun}.
{xunknown}. The sum of @b and an unknown number is {@b+x} @a time this amount is {@a(@b+x)} {trans}: {@a(@b+x)=@c} {solvex} to get the unknown number.
@a times the result of subtracting an unknown number from @b is @c. {findun}.
{xunknown}. Subtracting an unknown number from @b can be written like {@b-x} @a times this amount is {@a(@b-x)} {trans}: {@a(@b-x)=@c} {solvex} to get the unknown number.
@a times the sum of @b and @c times an unknown number is equal to @d times the sum of the unknown number and @e.
{xunknown}. @c times an unknown number is @cx. The sum of @b and @cx is {@b+@cx} The sum of an unknown number and @e is {x+@e} @d times this amount is @d(x+@e) {trans}: {@a(@b+@cx)=@d(x+@e)} {solvex} to get the unknown number.
When the sum of an unknown number and itself is multiplied by @a the result is @b. {findun}.
{xunknown}. The sum of an unknown number and itself is {x+x} ``multiplied by @a'' means {@a(x+x)} {trans}: {(x+x)@a=@b} {solvex} to get the unknown number.
A @a {dim} {long} is cut into two pieces. One piece is to be @b {dim} longer than the other piece. Find the length of each piece.
Let x be the length of one piece, and x+@b be the length of the other piece. The total length of both pieces must always equal the length of the entire object. {trans}: {x+(x+@b)=@a} {solvex} to get the length of one piece. The length of the other piece will be x+@b. {solvex} to get the unknown number.
A @a {dim} {long} is cut into two pieces. One piece is to be @b {dim} shorter than the other piece. Find the length of each piece.
Let x be the length of one piece, and x-@b be the length of the other piece. The total length of both pieces must always equal the total length of the entire object. {trans}: {x+(x-@b)=@a} {solvex} to get the unknown number.
A @a {dim} {long} is cut into two pieces. One piece is to be @b times the length of other piece. Find the length of each piece.
Let x be the length of one piece, and @bx be the length of the other piece. The total length of both pieces must always equal the length of the entire object. {trans}: {x+(@bx)=@a} {solvex} to get the length of one piece. @bx will be the length of the other piece.
{name} buys @a times more of {whatever1} than {whatever2}. Altogether, @b total items were purchased. How many of each were bought?
Let x be the number of {whatever2}. The amount of {whatever1} is @a times more of {whatever2} or {@ax} {trans}: {@ax+x=@b} {solvex} to get the number of {whatever2} she bought. The number of {whatever1} she bought will be @ax.
The sum of two consecutive integers is @a. What are the integers?
Let x=the first integer. Let x+1 be the next integer. {trans}: {x+(x+1)=@a} {solvex} to get the first integer. x+1 will be the second integer. {intwarn}.
The sum of three consecutive integers is @a. What are the integers?
Let x=the first integer, x+1=the second, and x+2=the third. {trans}: {x+(x+1)+(x+2)=@a} {solvex} to get the first integer. x+1 and x+2 will be the 2nd and 3rd integers. {intwarn}.
The sum of four consecutive integers is @a. What are the integers?
Let x=the first integer, x+1=the second, x+2=the third, and x+3=the fourth. {trans}: {x+(x+1)+(x+2)+(x+3)=@a} {solvex} to get the first integer. x+1 and x+2 will be the 2nd and 3rd integers. {intwarn}.
The sum of three consecutive odd integers is @a. What are the integers?
Let x=the first integer, x+2=the second, and x+4=the third. {trans}: {x+(x+2)+(x+4)=@a} {solvex} to get the first integer. x+2 and x+4 will be the 2nd and 3rd integers. {intwarn}.
The length of a rectangle is @a {dim} more than its width, and the perimeter is @b {dim}. Find the length and width.
Let L=the length, and W=the width. {trans}: {L=W+@a} The perimeter of a rectangle is L+L+W+W or 2L+2W, so {another} {2L+2W=@b} These are two equations and two unknowns. Solve for L and W.
The width of a rectangle is @a {dim} less than its length, and the perimeter is @b {dim}. Find the length and width.
Let L=the length, and W=the width. {trans}: {W=L-@a} The perimeter of a rectangle is L+L+W+W or 2L+2W, so {another}: {2L+2W=@b} These are two equations and two unknowns. Solve for L and W.
A @a {dim} piece of {long} is to be cut into two pieces. If one piece must be @b {dim} long, what will the length of the other piece be?
Let x be the length of the other piece. Then {trans}: {x+@b=@a}
@a times the sum of the first and third of three consecutive integers is @b times more than the second integer. Find the integers.
Let x=the first integer, x+1=the second integer, and x+2=the third integer. {trans}: {@a[x+(x+2)]=@b+(x+1)} {solvex} to get the first integer. x+1 and x+2 will be the 2nd and 3rd integers. {intwarn}.
When @a times the sum of @b and an unknown number is added to the unknown number, the result is the same as when @c is added to the unknown number. {findun}.
{xunknown}. The sum of @b and an unknown number is {@b+x} @a times this amount is {@a(@b+x)} Add this to the unknown number to get {@a(@b+x)+x} @c added to an unknown number is {@c+x} {trans}: {@a(@b+x)+x=x+@c} {solvex}
@a times the sum of @b and @c times an unknown number is equal to @d times the sum of @e times the unknown number and @f.
{xunknown}. @b times an unknown number is @bx. @c times an unknown number is @cx. @e times an unknown number is @ex. {trans}: {@a(@bx+@cx)=@d(@ex+@f)} {solvex}
