Dave and Peter went shopping. Dave bought 3 shirts and 2 pants and paid a total of $100.84. peter bought 4 shirt and 5 pants and paid total of $187. All pairs of pants cost the sam and all shirts cost the same. how much does one shirt cost? How much does one pair of pant cost?
a)Define Varible, b) write equation, c) solve, d) varify byour answer, e) answer the question in the conttext of the problem,
a)Define Varible, b) write equation, c) solve, d) varify byour answer, e) answer the question in the conttext of the problem,
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(a)
Let x = the cost of 1 shirt
Let y = the cost of 1 pair of pants
(b)
3x + 2y = 100.84
4x + 5y = 187
(c)
4x = 187 - 5y <--- subtract 5y from both sides of the bottom equation in (b)
x = (187 - 5y)/4 <--- solve for x by dividing by 4 on both sides
3[(187 - 5y)/4] + 2y = 100.84 <--- substitute x into the top equation in (b)
(561 - 15y)/4 + 2y = 100.84 <--- distribute the 3
(561 - 15y)/4 + 8y/4 = 100.84 <--- get a common denominator by multiplying 2y by 4/4
(561 - 15y + 8y)/4 = 100.84 <--- combine the fractions with common denominators
(561 - 7y)/4 = 100.84 <--- combine like terms
561 - 7y = 403.36 <--- multiply both sides by 4
-7y = -157.4 <--- subtract 561 from both sides
y = about 22.49 <--- divide both sides by -7
x = [187 - 5(22.49)]/4 <--- plug in y into the equation
x = (187 - 112.45)/4 <--- multiply
x = 74.55/4 <--- subtract
x = about 18.64 <--- divide
(d)
3(18.64) + 2(22.49) = 100.84 <--- plug x and y into first equation
100.9 almost = 100.84 <--- simplify
4(18.64) + 5(22.49) = 187 <--- plug x and y into second equation
187.01 almost = 187 <--- simplify
(e) One shirt costs $18.64. One pair of pants costs $22.49.
Let x = the cost of 1 shirt
Let y = the cost of 1 pair of pants
(b)
3x + 2y = 100.84
4x + 5y = 187
(c)
4x = 187 - 5y <--- subtract 5y from both sides of the bottom equation in (b)
x = (187 - 5y)/4 <--- solve for x by dividing by 4 on both sides
3[(187 - 5y)/4] + 2y = 100.84 <--- substitute x into the top equation in (b)
(561 - 15y)/4 + 2y = 100.84 <--- distribute the 3
(561 - 15y)/4 + 8y/4 = 100.84 <--- get a common denominator by multiplying 2y by 4/4
(561 - 15y + 8y)/4 = 100.84 <--- combine the fractions with common denominators
(561 - 7y)/4 = 100.84 <--- combine like terms
561 - 7y = 403.36 <--- multiply both sides by 4
-7y = -157.4 <--- subtract 561 from both sides
y = about 22.49 <--- divide both sides by -7
x = [187 - 5(22.49)]/4 <--- plug in y into the equation
x = (187 - 112.45)/4 <--- multiply
x = 74.55/4 <--- subtract
x = about 18.64 <--- divide
(d)
3(18.64) + 2(22.49) = 100.84 <--- plug x and y into first equation
100.9 almost = 100.84 <--- simplify
4(18.64) + 5(22.49) = 187 <--- plug x and y into second equation
187.01 almost = 187 <--- simplify
(e) One shirt costs $18.64. One pair of pants costs $22.49.