We want to know how much money each club raises for charity. Let's use the information from the exercise to create a system of linear equations that we can solve using the Elimination Method. We first need to find how many members there are in each club. Let's use x to represent the number of members of the cooking club x and y for the number of the woodshop club members.
Cooking Club: & x members
Woodshop Club: & y members
From the exercise, we know that the cooking club has three times as many members as the woodshop club. Let's write this as an equality.
x= 3 yWe also know that the difference of the number of members in the two clubs is 12. Since the cooking club has more members than the woodshop club, the cooking club has 12 more members than the woodshop club. Now we are ready to create another equation for the system.
x= y+ 12
Let's combine our equations to make a system of linear equations.
x=3y & (I) x=y+12 & (II)
Next, we will solve the system using the Elimination Method. Notice that the coefficients of the x-terms are the same. We can subtract Equation (II) from Equation (I) to get an equation in only one variable, y. Let's do it!
Finally, to find the amount each club raised for charity, we will multiply the number of members in the club by the amount they donated. The cooking club raised $ 5 for each member and the woodshop club raised $ 10 per member.
18* 5 = 90 6* 10=60
The cooking club raised $90 for charity, while the woodshop club raised $60.
