Calculating the Cost of Large and Small Bouquets at a Flower Shop

Solving for the Cost of Large and Small Bouquets

A flower shop sells large bouquets of slowers for $15 more than the price of small bouquets. On Mothers' Day last year, the shop earned $897 selling 32 small bouquets and 19 large bouqets.

Write and solve a linear system to find the cost of a large bouquet and the cost of a small bouquet.

Final answer:

The cost of a small bouquet is $12 and the cost of a large bouquet is $27.

Explanation:

To find the cost of a large bouquet and a small bouquet, we can set up a system of linear equations based on the given information. Let's assume the cost of a small bouquet is x dollars. According to the fact, the cost of a large bouquet would be x + $15 dollars.

Now, let's use the given information that the shop earned $897 by selling 32 small bouquets and 19 large bouquets. We can set up the following equation:

32x + 19(x + $15) = $897

Simplifying the equation, we get:

32x + 19x + $285 = $897

Combining like terms, we have:

51x + $285 = $897

Subtracting $285 from both sides of the equation, we get:

51x = $612

Dividing both sides of the equation by 51, we find:

x = $12

So, the cost of a small bouquet is $12. Substituting this value into the expression (x + $15), we can find the cost of a large bouquet:

$12 + $15 = $27