Cost of each smarties is 5 cents and cost of each jujubes is 2 cents.
Solution:
Let x be the smarties and y be the jujubes.
Cost of 6 smarties and 5 jujubes = 40 cents
⇒ 6x + 5y = 40 ---------- (1)
Cost of 3 smarties and 2 jujubes = 19 cents
⇒ 3x + 2y = 19 ---------- (2)
Subtract 3x on both sides.
⇒ 2y = 19 – 3x
Divide by 2 on both sides.
[tex]$\Rightarrow y=\frac{19-3x}{2}[/tex] ---------- (3)
Substitute this in equation (1), we get
[tex]$6x+5\left(\frac{19-3x}{2}\right)=40[/tex]
[tex]$6x+\left(\frac{95-15x}{2}\right)=40[/tex]
Multiply 6x by [tex]\frac{2}{2}[/tex], we get
[tex]$\frac{12x}{2} +\frac{95-15x}{2}=40[/tex]
Multiply by 2 on both sides, we get
12x + 95 – 15x = 80
–3x + 95 = 80
Subtract 95 from both sides, we get
–3x = –15
Divide by –3 on both sides,
x = 5
Substitute x = 5 in equation (3)
[tex]$\Rightarrow y=\frac{19-3(5)}{2}[/tex]
⇒ y = 2
Hence cost of each smarties is 5 cents and cost of each jujubes is 2 cents.
