Answer: the price of each apple is $2.25 and the price of each mango is $1.25
Step-by-step explanation:
Let x represent the price of one apple.
Let y represent the price of one mango.
Cameron went into a grocery store and bought 4 apples and 7 mangos, costing a total of $17.75. This means that
4x + 7y = 17.75 - - - - - - - - - - - - 1
Gavin went into the same grocery store and bought 2 apples and 5 mangos, costing a total of $10.75. This means that
2x + 5y = 10.75 - - - - - - - - - - - - -2
Multiplying equation 1 by 1 and equation 2 by 2, it becomes
4x + 7y = 17.75
4x + 10y = 21.5
Subtracting, it becomes
- 3y = - 3.75
y = - 3.75/ - 3
y = 1.25
Substituting y = 1.25 into equation 2, it becomes
2x + 5 × 1.25 = 10.75
2x + 6.25 = 10.75
2x = 10.75 - 6.25 = 4.5
x = 4.5/2 = 2.25
Answer:
Apples are $2.25 while mangoes are $1.25.
Step-by-step explanation:
We begin by converting these into simultaneous linear equations
4a + 7m = 17.75
2a + 5m = 10.75
from equation 1, we find a by
4a = 17.75 - 7m
a = 4.44 - 1.75m
We now put the value of a in equation 2
2 (4.44 - 1.75m) + 5m = 10.75
8.88 - 3.5m + 5m = 10.75
8.88 + 1.5m = 10.75
1.5m = 10.75 - 8.88
1.5m = 1.87
m = 1.25
we now put the value of m in equation 1
4a + 7(1.25) = 17.75
4a + 8.75 = 17.75
4a = 17.75 - 8.75
4a = 9
a = 2.25
