james bought 2 uniforms and 3 pairs of cleats for $275. ashley bought 4 uniforms and 2 pairs of cleats for $322.
Write and solve the system of equations
Let's say the cost of one uniform is U and the cost of one pair of cleats is C.
From the given information, we can write the following equations:
2U + 3C = 275 (equation 1)
4U + 2C = 322 (equation 2)
We can use the method of substitution to solve this system of equations.
Solve equation 1 for U:
2U = 275 - 3C
U = (275 - 3C)/2
Substitute this expression for U in equation 2:
4(275 - 3C)/2 + 2C = 322
2(275 - 3C) + 2C = 322
550 - 6C + 2C = 322
-4C = 322 - 550
-4C = -228
C = -228/-4
C = 57
Now substitute the value of C into equation 1 to find U:
2U + 3(57) = 275
2U + 171 = 275
2U = 275 - 171
2U = 104
U = 104/2
U = 52
Therefore, one uniform costs $52 and one pair of cleats costs $57.
this is incorrect. pick from:
(275,322)
(52,57)
or
(2,4)
Let's solve the system of equations:
2U + 3C = 275 (equation 1)
4U + 2C = 322 (equation 2)
We can solve this system of equations using either substitution or elimination. Let's use elimination.
Multiply equation 1 by 2 and equation 2 by 3 to eliminate the U terms:
4U + 6C = 550 (equation 3)
12U + 6C = 966 (equation 4)
Subtract equation 3 from equation 4 to eliminate the C terms:
12U + 6C - (4U + 6C) = 966 - 550
8U = 416
U = 416/8
U = 52
Substitute the value of U into equation 1 to solve for C:
2(52) + 3C = 275
104 + 3C = 275
3C = 275 - 104
3C = 171
C = 171/3
C = 57
Therefore, the correct answer is U = 52 and C = 57.