30. Last year the volleyball team paid $5 per pair for socks and $17 per pair fo

Question

30. Last year the volleyball team paid $5 per pair for socks and $17 per pair for shorts on a total purchase of $315. This 31. At a store, toothbrushes cost x dollars and bars of soap cost y dollars. One customer bought 2 toothbrushes and 1 bar of soap for $11. Another customer bought 6 toothbrushes and 5 bars of soap for $38. Both amounts do not include tax. Write and solve a system of equations forx hey spent $342 to buy the same number of pairs of and shorts because the socks now cost $6 a pair and the shorts cost $18. (a) Write a system that represents the number of pairs of socks and shorts each year. (b) How many of each were purchased each year? and y

Explanation / Answer

30) Let the no of socks = x

The no of sorts = y

A) 5x + 17y = 315

6x + 18y = 342

B) 6 * eqn(1) : 30x + 102y = 1890

5 * eqn(2) : 30x + 90y = 1710

Subtracting these two equations we will get

12y = 180

Or, y = 15

5x + 17 * 15 = 315

Or, 5x = 315 - 255

Or, 5x = 60

Or, x = 12

31) 2x + y = 11

Or, y = 11 - 2x

6x + 5y = 38

Or, 6x + 5(11 - 2x) = 38

Or, 6x + 55 - 10x = 38

Or, -4x = -17

Or, x = 17/4 = 4.25

y = 11 - 2 * 4.25

= 11 - 8.5 = 2.5

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