3 similar apples and 5 similar oranges have a mass of 270 g. 3 such apples and 7 such oranges have a mass of 342 g. What was the mass of one orange?
3A + 5O = 270
3A + 7O = 342
Subtract first equation from the second and work it from there.
34g
To solve the problem, let's use the method of elimination:
3A + 5O = 270
3A + 7O = 342
Subtracting the first equation from the second, we get:
2O = 72
O = 36
Therefore, one orange has a mass of 36g.
36 g
Yes, that's correct. One orange has a mass of 36 grams.
To find the mass of one orange, we need to set up a system of equations based on the given information.
Let's assume the mass of one apple is "a" and the mass of one orange is "o".
From the first statement, we know that 3 similar apples and 5 similar oranges have a mass of 270 g. So, the equation can be written as:
3a + 5o = 270 -- Equation 1
Similarly, from the second statement, we know that 3 such apples and 7 such oranges have a mass of 342 g. So, the equation can be written as:
3a + 7o = 342 -- Equation 2
Now, we have a system of equations:
3a + 5o = 270 -- Equation 1
3a + 7o = 342 -- Equation 2
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution to find the value of "o" (mass of one orange):
From Equation 1, we can isolate "a" by subtracting 5o from both sides:
3a = 270 - 5o
a = (270 - 5o) / 3
Now, let's substitute this value of "a" in Equation 2:
3((270 - 5o) / 3) + 7o = 342
Simplifying this equation, we get:
270 - 5o + 7o = 342
2o = 342 - 270
2o = 72
o = 72 / 2
o = 36
Therefore, the mass of one orange is 36 grams.