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Math 1
Focus on Translating Words into Equations
Name_______________________________
Translating Word Problems into a System of Equations—When a word problem involves more than one unknown quantity or
there are two (or more) equations or conditions to be satisfied, a system of equations may be used to solve the problem.
To translate the words into a system of equations, ask what two quantities are unknown and assign variables to them. The questions
posed in the problem may give you a clue. Then write equations using those variables and the conditions given in the problem.
Example: Translate the following problem into a system of equations. (Do not solve.)
At a local high school city championship basketball game, 1435 tickets were sold. A student admission ticket cost $1.50 and an adult
admission ticket cost $5.00. The total ticket receipts for the basketball game were $3552.50. How many of each type of ticket
were sold?
Solution: The question in the problem asks “how many of each type of ticket were sold?” Therefore, the two unknown
quantities are the number of student tickets (x) and the number of adult tickets (y). The problem gives one condition
related to the total number of tickets sold and another related to the total receipts from the ticket sales. Write one
equation (using the variables x and y) for each condition to obtain the following system:
Let x = # of student tickets
x + y = 1435
Let y = # of adult tickets
1.50x + 5.00y = 3552.50
Guided Problems: (Define variables. Write equations. Do not solve.)
1.
A grocer mixes peanuts that cost $2.49 per pound and walnuts that cost $3.89 per pound to make 100
pounds of a mixture that costs $3.19 per pound. How much of each kind of nut is put into the
mixture?
x  y  100
x  lbs of peanuts
y  lbs of walnuts
2.49 x  3.89 y  3.19 100 
2.
A certain brand of razor blades comes in packages of 6, 12, and 24 blades, costing $2, $3, and $4 per
package, respectively. A store sold 12 packages containing a total of 162 razor blades and took in
$35. How many packages of each type were sold?
x  Number of 6-blade packages sold
x  y  z  12
y  Number of 12-blade packages sold
6 x  12 y  24 z  162
z  Number of 24-blade packages sold
2 x  3 y  4 z  35
3.
Last season two running backs on the Steelers football team rushed for a combined total of
1550 yards. One rushed 4 times as many yards as the other. How many yards were rushed by
each player?
x = 1st player
x = 4y
nd
y = 2 player
x + y = 1550
Problem Set: Translate the following problems into a system of equations. (Do not solve.) Be sure to clearly
label your variables.
1.
A total of $15,000 is invested in two corporate bonds that pay 6.5% and 8% simple interest. The
investor wants an annual interest income of $1050 from the investments. How much should she invest
in each type of bond?
2.
Two pan pizzas and two beef burritos provide 3100 calories. One pan pizza and one beef burrito
provide 1550 calories. How many calories are in each item?
3.
Two medium eggs and one cup of ice cream contain 599 milligrams of cholesterol. One medium egg
and two cups of ice cream contain 376 milligrams of cholesterol (25 milligrams more than the
suggested daily intake of cholesterol). Determine the cholesterol content in each item.
4.
A particular Algebra text has a total of 1382 pages which is broken into two parts. The second
part of the book has 64 more pages than the first part. How many pages are in each part of
the book.
5.
A hotel has 150 rooms. Those with kitchen facilities rent for $100 per night and those without
kitchen facilities rent for $80 per night. On a night when the hotel was completely occupied, revenues
were $13,000. How many of each type of room does the hotel have?
6.
The calorie-nutrient information for an apple and an avocado is given in the table. How many of each
should be eaten to get exactly 1250 calories and 90 grams of carbohydrates?
Calories
Carbohydrates (grams)
One Apple
100
One Avacado
350
24
14
7.
When I multiply my first lucky number by 3 and my second lucky number by 2, the addition of the
resulting numbers produces a sum of 93. When I add twice my first lucky number to my second
lucky number, the sum is 53. What are my lucky numbers?
8.
At a college production of Evita, 500 tickets were sold. The ticket prices were $8, $10, and $12, and
the total income from ticket sales was $4700. How many ticket of each type were sold if the
combined number of $8 and $10 tickets sold was 4 times the number of $12 tickets sold? (Hint: This
problem has 3 unknowns and 3 conditions.)
9.
Two angles are complementary. The larger angle is 3 degrees less than twice the measure of
the smaller angle. Find the measure of each angle.