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.

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.

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