Answer:
Apple = Rs90
Grape = Rs70
Step-by-step explanation:
Given
Represent Apples with A and Grapes with G
Such that:
The ratio is
[tex]A : G =9:7[/tex]
And the price is
[tex]A = 20 + G[/tex]
Required
Determine the cost of 1 kg of each fruit
[tex]A : G =9:7[/tex]
Convert to fraction
[tex]\frac{A}{G} = \frac{9}{7}[/tex]
Cross Multiply
[tex]7A = 9G[/tex]
Make A the subject
[tex]A = \frac{9}{7}G[/tex]
Substitute [tex]\frac{9}{7}G[/tex] for A in [tex]A = 20 + G[/tex]
[tex]\frac{9}{7}G = 20 + G[/tex]
Collect Like Terms
[tex]\frac{9}{7}G - G = 20[/tex]
Take LCM
[tex]\frac{9G - 7G}{7}= 20[/tex]
[tex]\frac{2G}{7}= 20[/tex]
Multiply through by 7
[tex]7 * \frac{2G}{7}= 20 * 7[/tex]
[tex]2G= 20 * 7[/tex]
Divide through by 2
[tex]\frac{2G}{2} = \frac{20 * 7}{2}[/tex]
[tex]G = \frac{20 * 7}{2}[/tex]
[tex]G = 10 * 7[/tex]
[tex]G = 70[/tex]
Substitute 70 for G in [tex]A = \frac{9}{7}G[/tex]
[tex]A = \frac{9}{7} * 70[/tex]
[tex]A = 9 * 10[/tex]
[tex]A = 90[/tex]
