Question

Each gram of a mandarin orange has 0.26 mg of vitamin C and
0.13 mg of vitamin A. Each gram of a tomato has 0.13 mg of vitamin C
and 0.42 mg of vitamin A. How many grams of mandarin oranges and
tomatoes have 13 mg of vitamin C and 20.7 mg of vitamin A?

Answer 1

Let x be the number of grams of mandarin oranges and y be the number of grams of tomatoes.
The total amount of vitamin C is 0.26x + 0.13y.
The total amount of vitamin A is 0.13x + 0.42y.
We want to find x and y such that 0.26x + 0.13y = 13 and 0.13x + 0.42y = 20.7.
Multiplying the first equation by 100 and the second equation by 10, we get:
26x + 13y = 1300 and 13x + 42y = 207.
Multiplying the first equation by 3 and the second equation by 4, we get:
78x + 39y = 3900 and 52x + 168y = 828.
Subtracting the second equation from the first, we get:
(78x + 39y) - (52x + 168y) = 3900 - 828
26x - 129y = 3072
Solving this equation with the first equation, we have the following system of equations:
26x - 129y = 3072
26x + 13y = 1300
Subtracting the second equation from the first, we get:
(26x - 129y) - (26x + 13y) = 3072 - 1300
-142y = 1772
Dividing both sides of the equation by -142, we get:
y = -1772/-142
y = 12.5
Substituting the value of y into the first equation, we get:
26x - 129(12.5) = 3072
26x - 1612.5 = 3072
26x = 3072 + 1612.5
26x = 4684.5
Dividing both sides of the equation by 26, we get:
x = 4684.5/26
x = 180
Therefore, there are 180 grams of mandarin oranges and 12.5 grams of tomatoes that have 13 mg of vitamin C and 20.7 mg of vitamin A.