Question

Jaidee and Eugene are selling fruit for a school fundraiser. Customers can buy small boxes of tangerines and large boxes of tangerines. Jaidee sold 5 small boxes of tangerines and 4 large boxes of tangerines for a total of $130. Eugene sold 2 small boxes of tangerines and 5 large boxes of tangerines for a total of $120. What is the cost each of one small box of tangerines and one large box of tangerines?

Answer 1

This is going to take a while. First, set up equations for both Jaidee and Eugene. Jaidee's equation is $5s+4l=130$  s represents the cost of the small box of tangerines and $l$ represents the cost of the large box of tangerines. Eugene's equation is $2s+5l=120$ .  Next, I'm going to solve the equations through elimination. Multiply -2 by the first equation and multiply 5 by the second equation. $-2(5s+4l=130)=-10s-8l=-260$  Do the same for the second equation. $5(2s+5l=120)=10s+25l=600$ . Then add $10s-8l=-260+10s+25l=600$  This gives you $17l=340$ . Next divide on both sides  $\frac{17l}{17} =\frac{340}{17}$  this will give you $l=20$ . So you know what $l$ is. Next, plug in $l$ to $10s+25l=600$ which looks like this $10s+25(20)=600$. Solve 10s+500=600 = 10s+500-500=600-500 =10s=100 = 10s/10=100/10 = s=10 . So each box of small tangerines costs $10 and each box of large tangerines cost $20.