We can use the given information to create a system of equations. Then, solving the system for the variables will tell us how many papayas Tamara and Will sold together.
Writing a System of Equations
Let x be the number of papayas Tamara sold and y be the number of papayas Will sold. Now we will make a table and translate the verbal expressions to algebraic expressions.
Verbal Expression
Algebraic Expression
Earnings from papayas that Tamara sold for $5 each
5 x
Earnings from papayas that Will sold for $7 each
7 y
The total earning
147
Using the table, we can write our first equation. The sum of 5x and 7y should be equal to 147.
5 x + 7 y & = 147In a similar way, we can write another equation.
Verbal Expression
Algebraic Expression
Number of papayas Tamara sold
x
3 more papayas than the number of papayas Will sold
y+ 3
It is given that these expressions are equal.
x= y+ 3
Now we can write a system of equations.
5x+7y=147 & (I) x=y+3 & (II)
Solving the System of Equations
We will solve this system for the values of x and y using the Substitution Method. Specifically, we will substitute the second equation into the first equation and solve for y.
