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Let x = # of three-bedroom units, y = # of four-bedroom units.
From the condition, you have these 2 equations
x + y = 198 (1) (counting units)
3*x + 4*y = 710 (2) (counting rooms)
From equation (1), express y = 198 - x and substitute it into equation (2). You will get
3x + 4*(198-x) = 710.
Express x and calculate answer
x = = 82.
Then from equation (1), y = 198 - 82 = 116.
ANSWER. 82 three-bedroom units and 116 four-bedroom units.
CHECK. 3*82 + 4*116 = 710 rooms. ! Correct !
The problem solved using 2-equation setup and the Substitution method.
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It is a standard and typical ticket problem.
For ticket problems, read the lessons
- Using systems of equations to solve problems on tickets
- Three methods for solving standard (typical) problems on tickets
in this site.
From these lessons, learn on how to solve such problems once and for all.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".