A florist is making bouquets. Each small bouquet requires 2 roses, and each large bouquet … — SAT

A florist is making bouquets. Each small bouquet requires $2$ roses, and each large bouquet requires $5$ roses. The florist has at most $40$ roses available for these bouquets. Additionally, the florist wants to make more than $10$ bouquets in total. If $x$ represents the number of small bouquets and $y$ represents the number of large bouquets, which of the following systems of inequalities represents this situation?

A
$2x + 5y \geq 40$ and $x + y < 10$
B
$5x + 2y \leq 40$ and $x + y > 10$
$2x + 5y \leq 40$ and $x + y > 10$ Cevap
D
$2x + 5y \leq 10$ and $x + y > 40$

Cevap

The system of inequalities

2x + 5y \leq 40

and

x + y > 10

The correct system of inequalities matches the constraints given in the problem. The total number of roses used by

x

small bouquets and

y

large bouquets is

2x + 5y

. Since the florist has at most

40

roses, this is represented by

2x + 5y \leq 40

. The total number of bouquets is

x + y

. Since the florist wants to make more than

10

bouquets, this is represented by

x + y > 10

Adım Adım Çözüm

Identify the inequality representing the constraint on the total number of roses.

2x + 5y \leq 40

Each small bouquet uses

2

roses (

2x

) and each large bouquet uses

5

roses (

5y

). The total roses must be 'at most'

40

, which corresponds to the inequality symbol

\leq

Identify the inequality representing the constraint on the total number of bouquets.

x + y > 10

The total number of bouquets is the sum of small bouquets (

x

) and large bouquets (

y

). The florist wants 'more than'

10

bouquets, which corresponds to the inequality symbol

>

Combine the two inequalities into a single system.

The system is

2x + 5y \leq 40

and

x + y > 10

Both conditions must be met simultaneously.

Anahtar Kavram

Translating real-world constraints into a system of linear inequalities in two variables.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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Konular

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