Write the equation

Question

The French club sold rose bouquets and chocolate hearts for Valentine's Day. The roses sold for $5 and the hearts sold for $3. The number of bouquets sold was 15 more than the number of hearts sold. If the club collecred a total of $339, how many of each gift was sold? Write a system of equations and solve

Answer 1

Let:

 

r=number of roses sold

h=number of chocolate hearts sold

r=h+15.......number of roses sold is 15 more than hearts (given info)

 

 

Then:

5r+3h=339

5(h+15)+3h=339.......substitute expression for variable "r"

  5h+75+3h=339........distribute

        8h+75=339........combine like terms

              8h=264........subtract 75 from both sides

                h=33..........divide both sides by 8

 

So, 33 chocolate hearts were sold.

 

Now substitute h=33 into the equation r=h+15 to arrive

at the number of roses sold.....

r=33+15

r=48

 

So, 48 roses were sold

 

Now let's check our work.  Substitute the two values into 

the equation for $$cost.....

         5r+3h=339

5(48)+3(33)=339

       240+99=339

             339=339........check√, our values are correct

 

Summary....48 roses and 33 chocolates hearts were sold.

 

Answer 2

Let number of roses be x

number of hearts  y

Given: x-y = 15  ...   (1)

5x + 3y = 339    ...   (2)

 

Solution:

 

From (1):  x=y+15

Plug in (2):

5(y+15) +3y = 339

5y +75 +3y =339

8y = 339-75

y = (339-75)/8

y=33 number of hearts

x=33+15 = 48 number of roses