1) If Agnes buys six apples, five bananas, and two oranges, the cost will be $2.85. If she

buys three apples, seven bananas, and four oranges, the cost will be $2.70. If apples are 1

cent less than twice as expensive as oranges, what is the cost of each?

One apple cost 27 cent or $0.27

One banana cost 19 cent or $0.19

One orange cost 14 cent or $0.14

Step-by-step explanation:

Let x represent the cost of one apple

Let y represent the cost of one banana

Let z represent the cost of one orange

Since the monetary unit is both in dollars and cents, we use the cent (¢) unit.

1 dollar ($) = 100 cent (¢)

Therefore, $2.85 and $2.70 will be 285¢ and 270¢ respectively.

According to the question, Agnes buys six apples, five bananas, and two oranges with a total cost of 285¢. Mathematically, this means:

6x + 5y + 2z = 285¢ eqn1

Agnes buys three apples, seven bananas, and four oranges, which cost 270¢ in total. Mathematically,

3x + 7y + 4z = 270¢ eqn2

The question further states that apples are 1

cent less than twice the cost of oranges. This mathematically means:

x = 2z - 1 eqn3

We use simultaneous equation to solve this, but we have to reduce the variables in each equation 1&2 to 2 by substituting eqn3 into both equations 1&2 i.e.

6x + 5y + 2z = 285 eqn1

6(2z-1) + 5y + 2z = 285

12z - 6 + 5y + 2z = 285

14z + 5y = 285 + 6

14z + 5y = 291 eqn4

3x + 7y + 4z = 270 eqn2

3(2z-1) + 7y + 4z = 270

6z - 3 + 7y + 4z = 270

10z + 7y = 270 + 3

10z + 7y = 273 eqn5

Now we can simultaneously solve equations 4&5 using elimination method.

14z + 5y = 291

10z + 7y = 273

We multiply eqns 4 and 5 by 7 and 5 respectively in order to eliminate variable y

7 × 14z + 5y = 291

5 × 10z + 7y = 273

98z + 35y = 2037

50z + 35y = 1365

We subtract to have

48z = 672

z = 672/48

z = 14

If z is 14, we substitute the value of z into eqn3;

x = 2z - 1

x = 2(14) - 1

x = 28 - 1

x = 27

If z= 14 and x=27, we substitute both values into eqn 2

3x + 7y + 4z = 270

3(27) + 7y + 4(14) = 270

81 + 7y + 56 = 270

137 + 7y = 270

Collect like terms

7y = 270-137

7y = 133

y= 133/7

y = 19

Hence, z= 14, y=19 and x=27.

This means that the cost of one apple, one banana and one orange is 27¢, 19¢ and 14¢ respectively.

828. all there is to it!

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