The mass of a bolt with a nut is 49g, and the mass of four bolts is 70g more than the mass of five nuts. What is the mass of a bolt and the mass of one nut?
Let’s compose a system of equations in which we denote the mass of the bolt as x grams, and the weight of the nut as in grams.
Thus, we get:
x + y = 49 g.
4 * x – 5 * y = 70 g.
We express the weight of one bolt x from the first equation of the system.
x = 49 – y.
Substitute the found value into the second equation.
4 * (49 – y) – 5 * y = 70.
196 – 4 * y – 5 * y = 70.
9 * y = 126.
y = 126/9 = 14 grams (weight of one nut).
Find the mass of the bolt.
x = 49 – 14 = 35 grams.
Answer: The bolt weighs 35 grams, the nut 14 grams.
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