$39$ . Uncle Joe used a total of $6480$ sticks of satay over $3$ days. He used $220$ more sticks of satay on Day $1$ than on Day $2$ and $100$ more sticks of satay on Day $2$ than on Day $3$ . How many sticks of satay did he use on Day $1$ ?

Full solution

39

. Uncle Joe used a total of

6480

sticks of satay over

3

days. He used

220

more sticks of satay on Day

1

than on Day

2

and

100

more sticks of satay on Day

2

than on Day

3

. How many sticks of satay did he use on Day

1

Define Variables: Let's call the number of sticks used on Day $3$ as $x$ . So on Day $2$ , Uncle Joe used $x + 100$ sticks, and on Day $1$ , he used $(x + 100) + 220$ sticks. Now we can write an equation for the total sticks used over the $3$ days. $\newline$ $x + (x + 100) + ((x + 100) + 220) = 6480$
Simplify Equation: Now, let's simplify the equation. $3x + 420 = 6480$
Subtract $420$ : Next, we subtract $420$ from both sides to solve for $3x$ . $\newline$ $3x = 6480 - 420$ $\newline$ $3x = 6060$
Divide by $3$ : Now, we divide both sides by $3$ to find $x$ . $x = \frac{6060}{3}$ $x = 2020$
Find Day $1$ Sticks: Since $x$ is the number of sticks used on Day $3$ , we can now find out how many sticks were used on Day $1$ . $\newline$ Day $1$ sticks = $(2020 + 100) + 220$ $\newline$ Day $1$ sticks = $2120 + 220$ $\newline$ Day $1$ sticks = $2340$