Did I set this up right?
6x+3y=510
9x+9y=1080
Val sold 2 types of Valentine's day bouquets: Deluxe and Special. Each Deluxe Bouquet used 6 roses and 9 carnations while each Special Bouquet used 3 roses and 9 carnations. Val has 510 roses and 1080 carnations. If Val used all of these flowers, how many Deluxe and how many special bouquets did she sell? Define variables,set up equation, and solve.
Oops I meant 6x+9y=510, 3x+9y=1080
Who knows, you didn't define your variables
if x is the number of Deluxe bouquets, and
y is the number of Specials, then
6x + 3y = 510 or 2x + y = 170
9x + 9y = 1080 or x + y = 120
easy to solve, subtract the last two equations etc
To set up the equations for this problem, let's define two variables:
Let x represent the number of Deluxe Bouquets sold.
Let y represent the number of Special Bouquets sold.
Based on the information given, each Deluxe Bouquet uses 6 roses and 9 carnations, while each Special Bouquet uses 3 roses and 9 carnations. We know that Val has a total of 510 roses and 1080 carnations.
So we can set up the following equations:
6x + 3y = 510 (equation 1 - represents the total number of roses used)
9x + 9y = 1080 (equation 2 - represents the total number of carnations used)
Now we can solve these equations to find the values of x and y.
To solve these equations, we can use the method of substitution or elimination. Let's use the elimination method here:
First, multiply equation 1 by 3 and equation 2 by 2 to make the coefficients of y equal:
18x + 9y = 1530 (equation 3)
18x + 18y = 2160 (equation 4)
Now subtract equation 3 from equation 4 to eliminate x:
18x + 18y - (18x + 9y) = 2160 - 1530
18y - 9y = 630
9y = 630
Dividing both sides of the equation by 9:
y = 70
Substitute the value of y in equation 1:
6x + 3(70) = 510
6x + 210 = 510
6x = 510 - 210
6x = 300
Dividing both sides of the equation by 6:
x = 50
Therefore, Val sold 50 Deluxe Bouquets and 70 Special Bouquets.