To save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother sid he can work no more than 15 hours to ensure he keeps up with his homework. Tom needs to make at least $75 to cover prom expenses. If d represents the number of hours walking his neighbor's dog and c represents the number of hours washing cars, which system of inequalities represents this situation? a

\large 6d+7.5c\le15

\large d+c\ge75

b

\large 6d+7.5c\le75

\large d+c\ge15

c

\large 6d+7.5c\ge75

\large d+c\le15

d

\large 6d+7.5c\ge15

\large d+c\le75

d + c ≤ 15

6*d + 7.50*c≥ 75

Step-by-step explanation:

  Mathematical inequality is that proposition that relates two algebraic expressions whose values are different. It is a proposition of relation between two different elements, either by greater, lesser, greater or equal inequality, or less or equal.

In other words, an inequality is obtained by writing two numerical or algebraic expressions related to any of the symbols>, <, ≥ or ≤.

You know Tom's mom said that he can't work more than 15 hours to make sure he keeps up with his homework. That is, the number of hours walking the neighbor's dog added to the car wash should not exceed 15 hours, that is, it must be less than or equal to that amount. If d represents the number of hours walking your neighbor's dog and c represents the number of hours washing cars, then it is possible to represent this by the following inequality:

d + c ≤ 15 Inequality (A)

On the other hand, you know that Tom needs to earn at least $ 75 to cover the expenses of this weekend's prom. In other words, the money earned by walking dogs added to that earned by washing cars must be equal to or greater than $ 75. If Tom will walk his neighbor's dog for $ 6 an hour and wash cars for $ 7.50 an hour, then $ 6*d is the money earned walking dogs and $ 7.50*c is the money earned from washing cars. So this is represented by the inequality:

6*d + 7.50*c≥ 75 Inequality (B)

Then the system of inequalities that represents this situation is given by the Inequation (A) and the Inequation (B)

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step-by-step explanation:

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option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,