I know I put this question yesterday but I tried it again with a new understanding.
Val sold 2 types of Valentine's day bouquets: deluxe and special. For deluxe, there were 6 roses and 9 carnations. For the special bouquet, there were 3 roses and 9 carnations. Val had 510 roses and 1080 carnations. If she used all of these flowers, how many deluxe and how many special bouquets did she sell? Define variable(s), set up equation(s) and solve.
I think my variables are x=roses and y= carnations.
I think the equation would look like:
3s+6d=510
9s+9d=1080
She sold 50 deluxe bouquets and 70 special bouquets.
I did this same question yesterday, but cannot find it.
Why are you defining your unknown in terms of x and y, and then use
s and d in the equations ??
Furthermore, the number of roses and number of carnations are known , so why define them ?
What we are supposed to find is the number of deluxe and the number of special bouquets.
So let x be the number of deluxe , and
let y be the number of special bouquets.
6x + 3y = 510
9x + 9y = 1080
now solve for x and y, using the method you learned.
Btw, you should have know that either your equations or your answers, or even both were wrong, since your solution does not satisfy your equation.
Great job identifying the variables and setting up the equations! You're on the right track.
To solve the problem, we'll solve the system of equations using substitution or elimination.
Let's use substitution. We can solve the first equation for s (special bouquet) in terms of d (deluxe bouquet):
3s + 6d = 510
3s = 510 - 6d
s = (510 - 6d) / 3
s = 170 - 2d
Now we substitute this expression for s into the second equation:
9s + 9d = 1080
9(170 - 2d) + 9d = 1080
1530 - 18d + 9d = 1080
1530 - 9d = 1080
-9d = 1080 - 1530
-9d = -450
d = -450 / -9
d = 50
We have found the value of d (deluxe bouquet), which is 50. Now, substitute this value back into the first equation to find s (special bouquet):
3s + 6d = 510
3s + 6(50) = 510
3s + 300 = 510
3s = 510 - 300
3s = 210
s = 210 / 3
s = 70
So, Val sold 50 deluxe bouquets and 70 special bouquets.
Don't forget to check your answer by plugging the values of s and d back into both equations to make sure they satisfy both equations.