Arestaurant 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

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.

its the second choice.

step-by-step explanation:

the elements in the range will be 7 less than the elements in the domain.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .