Question

A restaurant catered a party for 45 people. A child’s dinner (c) cost $15 and an adult’s dinner (a) cost $25. The total cost of the dinner was $1,015. How many children and adults were at the party? Use the table to guess and check.

A. 9 adults and 36 children
B. 10 adults and 35 children
C. 34 adults and 11 children
D. 36 adults and 9 children

Answer 1

The answer is C. I hope this helps. :)

Answer 2

Answer:

Option C is correct.

Step-by-step explanation:

Number of children at party = 45

Dinner cost of a child = $ 15

Dinner cost of an Adult = $ 25

Total cost of dinner = $ 1015

let x be the number of children in party.

y be the number of adults in party.

According tot the Question,

x + y = 45 ....................(1)

15x + 25y = 1015

3x + 5y = 203 ..................(2)

Now with given option,

Option A,

x = 36   and y = 9

In Equation (1),

LHS = 9 + 36 = 45 = RHS

In Equation (2),

LHS = 3(36) + 5(6) = 108 + 30 = 138 ≠ RHS

Thus this is not the solution.

Option B,

x = 35   and y = 10

In Equation (1),

LHS = 10 + 35 = 45 = RHS

In Equation (2),

LHS = 3(10) + 5(35) = 30 + 175 = 205 ≠ RHS

Thus this is not the solution.

Option C,

x = 11   and y = 34

In Equation (1),

LHS = 11 + 34 = 45 = RHS

In Equation (2),

LHS = 3(11) + 5(34) = 33 + 170 = 203 = RHS

Thus this is the solution.

Option D,

x = 9   and y = 36

In Equation (1),

LHS = 9 + 36 = 45 = RHS

In Equation (2),

LHS = 3(9) + 5(36) = 27 + 180 = 207 ≠ RHS

Thus this is not the solution.

Therefore, Option C is correct.