Asnack stand sold hot dogs and chips at a recent game. the hot dogs cost $2.50 and the snacks cost $0.75. after the game, they tallied 175 transactions totaling $262.50. represent the linear system in an augmented matrix:

x = hot dogs

y = snacks

x +y = 175

x = 175-y

2.50x + 0.75y = 262.50

2.50(175-y) +0.75y = 262.50

437.50-2.50y + 0.75y = 262.50

-1.75y = -175

y = -175 / -1.75 = 100

100 snacks & 75 hot dogs

The number of hot dogs sold is 75 while the number of snacks sold is 100.

Based on the information, the equation to solve the question will be:

x + y = 175 i

2.50x + 0.75y = 262.50 ii

From equation i, x = 175 - y.

We'll put the value of x into 2.50x + 0.75y = 262.50 and this will be:

2.50x + 0.75y = 262.50

2.50(175 - y) + 0.75y = 262.50

437.50 - 2.50y + 0.75y = 262.50

Collect like terms

-2.50y + 0.75y = 262.50 - 437.50

-1.75y = -175

y = 175/1.75

y = 100

The number of snacks sold is 100.

Since x + y = 175

x = 175 - 100

x = 75

The number of hot dogs sold is 75

Therefore, 75 hot dogs and 100 snacks were sold.

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