Answer:
The cost of grapefruits per box is $3, The cost of strawberries per box is $2.5
The cost of avocados per box is $6
Step-by-step explanation:
Let us represent the price of Grapefruits per box = g
Strawberries per box = s
Avocados per box = a
Alyssa buys two boxes of strawberries and three boxes of avocados and spent $23
2s + 3a = 23 ....... Equation 1
a = 23 - 2s
London buys three boxes of grapefruit and four boxes of strawberries in Spain $19
3g + 4s = 19 ....... Equation 2
Tina buys seven boxes of grapefruit and five boxes of avocados in Spencer $51
7g + 5a = 51..... Equation 3
2s + 3a = 23 ....... Equation 1
3g + 4s = 19 ....... Equation 2
7g + 5a = 51..... Equation 3
Substituting 3a = 23 - 2s in Equation 3
a = 23 - 2s/3
7g + 5(23 - 2s/3) = 51
7g +( 115 - 10s/3) = 51
Multiply through by 3
7g × 3 + ( 115 - 10s/3) × 3 = 51 × 3
21g + 115 - 10s = 153
21g -10s = 38 ........ Equation 4
Combining Equation 2 and 4
3g + 4s = 19 ....... Equation 2 × 10
21g -10s = 38 ........ Equation 4 × 4
30 + 40s = 190.. Equation 5
84g - 40s = 152 .... Equation 6
We Add Equation 5 and Equation 6 to eliminate s
114g = 342
g = 342/114
g = $3
To find s, cost 0f straw berries
g = $3
3g + 4s = 19 ....... Equation 2
3(3) + 4s = 19
9 + 4s = 19
4s = 19 -9
4s = 10
s = 10/4
s = $2.5
For find a, the cost of avocados.
7g + 5a = 51..... Equation 3
g = $3
7(3) + 5a = 51
21 + 5a = 51
5a = 51 - 21
5a = 30
a = 30/5
a = $6
g =$ 3, s =$ 2.5 and a = $6.
Therefore:
The cost of grapefruits per box is $3.
The cost of strawberries per box is $2.5 and
The cost of avocados per box is $6
