There are 16 roses, 2 tulips, and 6 lilies in each Autumn Classic bouquet
Step-by-step explanation:
The information in the problem:
1. You have $610 to make five Autumn Classic bouquets for your friends
2. Each bouquet has 24 flowers
3. Roses cost $6 each, tulips cost $4 each, and lilies cost $3 each
4. You want to have twice as many roses as the other 2 flowers
combined in each bouquet
We need to find how many roses, tulips, and lilies you include in each
Autumn Classic bouquet
Assume that the number of roses is R, the number of tulips is T and
the number of lilies is L in each bouquet
∵ There are R roses, T tulips and L lilies in each bouquet
∵ The number of flowers in each bouquet is 24
∵ R + T + L = 24 ⇒ (1)
∵ He has $610 to make the 5 bouquets
∴ He spends in each bouquet = 610 ÷ 5 = $122
∵ Each rose costs $6
∵ Each tulip costs $4
∵ Each Lillie costs $3
∴ 6R + 4T + 3L = 122 ⇒ (2)
∵ The number of roses is twice the sum of the numbers of the
other 2 flowers
∴ R = 2(T + L)
∴ R = 2T + 2L ⇒ (3)
Substitute R in equations (1) and (2) by equation (3)
∵ (2T + 2L) + T + L = 24
- Add like terms in the left hand side
∴ 3T + 3L = 24 ⇒ (4)
∵ 6(2T + 2L) + 4T + 3L = 122
∴ 12T + 12L + 4T + 3L = 122
- Add like terms in the left hand side
∴ 16T + 15L = 122 ⇒ (5)
Let us solve the system of equations to find the values of T and L
Multiply equation (4) by -5 to eliminate L
∵ (-5)(3T) + (-5)(3L) = (-5)(24)
∴ -15T - 15L = -120 ⇒ (6)
Add equations (5) and (6)
∴ T = 2
- Substitute the value of T in equation (4) to find L
∵ 3(2) + 3L = 24
∴ 6 + 3L = 24
- Subtract 6 from both sides
∴ 3L = 18
- Divide both sides by 3
∴ L = 6
Substitute the values of T and L in equation (3) to find R
∵ R = 2T + 2L ⇒ (3)
∴ R = 2(2) + 2(6)
∴ R = 4 + 12
∴ R = 16
There are 16 roses, 2 tulips, and 6 lilies in each Autumn Classic bouquet
Learn more:
You can learn more about solving the system of equations in
brainly.com/question/13168205
brainly.com/question/9045597
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