Question

Initially, there were equal amount of roses and tulips at a store. Each bouquet was made with 3 roses and 4 tulips. After the bouquets were all made, there were 30 roses and 18 tulips left in the store. How many bouquets were made?

Answer 1

12 bouquets were made

Initially : 66 roses and 66 tulips

Explanation:

T=total amount of flowers

b=bouquets made

T/2-3b = 30 (half of total minus 3 roses per bouquet equal 30)

T/2-4b = 18 (half of total minus 4 tulips per bouquet equal 18)

I will multiply the second by -1 (elimination method)

T/2 - 3b = 30

-T/2 + 4b= -18

Add both:

0+ 1b = 12 (12 bouquets)

ROSES TULIPS

(T/2)-(3*12)=30 (T/2)-(4*12)=18

T/2 -36 = 30 T-48=18

T /2 = 66 (66 roses) T/2= 66 (66 tulips)

T/2 + T/2 = TOTAL= 132 flowers initially

36 + 48 + 30 + 18 = 132

Answer 2

12 bouquets

Explanation:

Let there be x number of roses and x number of tulips initially at the store. Each bouquet was made with 3 roses and 4 tulips. Assume that y bouquets were made in total.

If each bouquet was made with 3 roses and 4 tulips, then y bouquets will be made with 3y roses and 4y tulips.

After the bouquets were all made, there were 30 roses and 18 tulips left in the store. This means, if we subtract number of roses that were used in bouquets from total number of roses, the result must be 30. Likewise, for tulips the result would be 18. This can be represented as:

x - 3y = 30 Equation 1

x - 4y = 18 Equation 2

Subtracting Equation 2 from Equation 1, we get:

x - 3y - (x - 4y) = 30 - 18

x - 3y - x + 4y = 12

y = 12

Since y represents the number of bouquets made, we can conclude that 12 bouquets were made in the store.