A florist sells carnations for 1.50 each and roses for 3.00 each. The equation 1.50c + 3.0… — SAT

A florist sells carnations for $1.50$ each and roses for $3.00$ each. The equation $1.50c + 3.00r = 45.00$ represents the possible number of carnations, $c$ , and roses, $r$ , that a customer can buy for exactly $45.00$ . If the customer buys 8 carnations, how many roses can they buy?

Answer: 11

Answer

To find the number of roses the customer can buy, substitute the number of carnations bought, which is 8, for

c

in the given equation. This yields

1.50(8) + 3.00r = 45.00

. Simplifying the product gives

12.00 + 3.00r = 45.00

. Subtracting 12.00 from both sides of the equation gives

3.00r = 33.00

. Finally, dividing both sides by 3.00 yields

r = 11

. Thus, the customer can buy 11 roses.

Step-by-Step Solution

Substitute the given value for carnations,

c = 8

, into the linear equation.

1.50(8) + 3.00r = 45.00

We are given that the customer buys 8 carnations, so

c

is replaced by 8 to solve for the number of roses,

r

Multiply

1.50

8

to simplify the term.

12.00 + 3.00r = 45.00

Simplifying the constant term on the left side of the equation.

Subtract

12.00

from both sides of the equation to isolate the term with

r

3.00r = 33.00

To solve for

r

, we must get the term

3.00r

by itself on one side.

Divide both sides of the equation by

3.00

to solve for

r

r = 11

Dividing isolates the variable

r

Key Concept

Solving a linear equation in two variables by substitution when one variable's value is known.

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