The price of each uniform is $145
The price of each pair of cleats is $16
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Simultaneous Linear Equations could be solved by using several methods such as :
If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.
Let us tackle the problem!
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Complete Question:
Rigo and Ian went shopping for soccer cleats and practice uniforms. Rigo spent $451, before taxes, and purchased three uniforms and one pair of cleats. Ian spent $757, before taxes, and purchased five uniforms and two pair of cleats. Assuming all the uniforms cost the same amount and all the cleats cost the same amount, find the price of each uniform and each pair of cleats!
Let:
The Price of Each Uniform = U
The Price of Each Pair of Cleats = C
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Rigo spent $451, before taxes, and purchased three uniforms and one pair of cleats.
[tex]3U + C = 451[/tex] → Equation A
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Ian spent $757, before taxes, and purchased five uniforms and two pair of cleats.
[tex]5U + 2C = 757[/tex] → Equation B
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Let's calculate → 2(Equation A) - (Equation B)
[tex]2( 3U + C ) - (5U + 2C) = 2(451) - 757[/tex]
[tex]6U + 2C - 5U - 2C = 145[/tex]
[tex]U = \$ 145[/tex]
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[tex]3U + C = 451[/tex]
[tex]3(145) + C = 451[/tex]
[tex]C = 451 - 3(145)[/tex]
[tex]C = 451 - 435)[/tex]
[tex]C = \$ 16[/tex]
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Grade: High School
Subject: Mathematics
Chapter: Simultaneous Linear Equations
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Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations
#LearnWithBrainly
part A:
let u be the cost of each uniform and c be the cost of each pair of cleats .
rigo bought 3 uniforms and 1 pair of cleats so he spent 3u dollars on uniforms and c dollars on cleats .the total amount he spent was then 3u + c =451.
lan bought 5 uniforms and 2 pairs of cleats so he spent 5u dollars on uniforms and 2c dollars on cleats .the total amount he spent was then 5u +2c =757.
the system of equations is then
{3u + c = 451
{5u + 2c =757
part B :
to use the elimination method ,one of the variables terms in each equation must have opposite coefficients.the second equation has a coefficient of 2 for the c term so multiply the first equation by -2 .this gives -6u - 2c = -902 .add this new equation to 5u + 2c =757 to eliminate c and then solve for u :
5u + 2c =757
-6u - 2c = -902
-u = -145
u =145
substitute u= 145 into 3u +c=451 and solve for c;
3u +c = 451
3 (145) + c = 451
435 + c =451
c = 16
therefore ,the price of each uniform is $145 and the price for each pair of cleats is $16.
