Answer:
1 bush costs $10.67 (2d.p.) and 1 tree costs $0.33 (2d.p.)
Step-by-step explanation:
Let's assume the price of a bush is b and the price of a tree is t.
Therefore we can turn these purchases into two equations:
[tex]Edward:\ \ 5b+2t=54\\Byran:\ \ 8b+2t=86[/tex]
1. Cost of a bush
Since the cost between these two equations is affected by the number of bushes we can figure out the price of one bush:
[tex]8b-5b=86-54\\=3b=32\\\therefore b=\frac{32}{3}\ or\ 10.67\ (2d.p.)[/tex]
Therefore the cost of one bush is $10.67.
2. Cost of a tree
We can now use substitution to work out the value of one tree, let's use 5b+2t=54:
[tex]5(\frac{32}{3}) +2t =54\\\\\frac{160}{3} +2t=54\\\\2t=\frac{2}{3} \\\\t=\frac{1}{3} \ or\ 0.33\ (2d.p.)[/tex]
Therefore the cost of a tree is $0.33.
Check:
Let's now check these values to make sure our values are correct using the equation 8b+2t to see if it equals 86:
[tex]8(\frac{32}{3} )+2(\frac{1}{3})\\\\\frac{256}{3}+\frac{2}{3} \\=\$86[/tex]
Note: When using the approximate value it equals $86.02 but answering of course uses the approximate value.
Hope this helps!!!
