Two numbers are in the ratio @a to @b. Their sum is @c. Find the two numbers.
Let x=the first number and y=the second number. {trans} {x/y=@a/@b} {another} {x+y=@c} These are two equations and two unknowns and can be solved for x and y. Hint: Solve Equation 1 for x, and plug this into Equation 2, and solve for y. Then get x using this result from either equation.
The length and width of a rectangle are in the ratio of @a to @b. The perimeter is @c. Find the length and width.
Let L=the length, and W=the width. {trans} {L/W=@a/@b} The perimeter of a rectangle is 2L+2W, so {another} {2L+2W=@c} These are two equations and two unknowns that can be solved for L and W. Hint: Solve Equation 1 for L, and plug this into Equation 2, then solve for W. Once you have W, plug it into Equation 1 to find L.
The amounts {name} spends for food, rent, and clothing are in the ratio @a:@b:@c. An average of $@d per month are spent each month on these three items. What is spent on each item in a month?
Let f=the amount spent on food, r=the amount spent on rent, and c=the amount spent on clothing. According to your problem f:r:c=@a:@b:@c. {trans} {f+r+c=@d} {another} {f/r=@a/@b} {another} {c/r=@c/@b} Use Equations 2 and 3 to eliminate f and c in Equation 1, then solve Equation 1 for r. Once you have r, use Equations 2 and 3 to find f and c.
Divide @a into two parts whose ratio is @b to @c.
Let x=the first part, let y=the second part. According to your problem x:y=@b:@c. {trans} {x+y=@a} {another} {x/y=@b/@c} Solve Equation 2 for x and plug this into Equation 1. Then solve Equation 1 for y to get the second part. Plug this result into Equation 2 to get x, the first result.
The three sides of a triangle are in the ratio @a:@b:@c. The perimeter of the triangle is @d {dim}. Find the three sides.
Let x=the first side, y=the second side, and z=the third side. According to your problem x:y:z=@a:@b:@c. {trans} {x+y+z=@d} {another} {x/z=@a/@c} {another} {y/z=@b/@c} Solve Equations 2 and 3 for x and y and plug these results into Equation 1. Now solve Equation 1 for z. Plug this result into Equations 1 and 2 to get x and y.
An uncle divided $@a among his three nephews in the ratio @b:@c:@d. How much did each receive?
Let x=the amount nephew #1 got, y=the amount nephew #2 got, and z=the amount nephew #3 got. According to your problem, the amount each got is in the ratio x:y:z=@b:@c:@d. {trans} {x+y+z=@a} {another} {x/z=@b/@d} {another} {y/z=@c/@d} Solve Equations 2 and 3 for x and y and plug these results into Equation 1. Now solve Equation 1 for z. Plug this result into Equations 1 and 2 to get x and y.
A patio floor was made with a cement-sand-gravel ratio of @a:@b:@c. If @d cubic {dim} of gravel were used, how much sand and cement were used?
Let x=the amount of cement, y=the amount of sand, and z=the amount of gravel. According to your problem, the amount of each used was in the ratio x:y:z=@a:@b:@c. {trans} {x+y+z=@d} {another} {x/z=@a/@c} {another} {y/z=@b/@c} Solve Equations 2 and 3 for x and y and plug these results into Equation 1. Now solve Equation 1 for z. Plug this result into Equations 1 and 2 to get x and y.
A restaurant served @a dinners. For every @b dinners served, @c were seafood. How many seafood dinners were served?
Let x=the amount of seafood dinners served, y=the amount of all other dinners. {trans} {x+y=@a} {another} {y/x=@b/@c} Now, solve Equation 2 for y, and plug this result into Equation 1 and solve for x. This is the number of seafood dinners served.
{name} drives @a miles in @b hours. Express the rate of mile to hours as a fraction.
{trans} {rate=@a/@b} The rate as a fraction is @a/@b.
If $@a was spent for carpeting that cost @b <sup>dollars</sup>/<sub>square {dim}</sub>, how many square yards were purchased?
Let x=the number of square yards of carpet purchased. According to your problem the cost ratio of dollars to carpet is @b dollars:1 square {dim}. But in this problem, $@a dollars were spent. So, {@a/x=@b/1} Solve this equation for x to get the number of square yards of carpet purchased.
