A man spend one third of his wages on food and one fifth on rent.
A. What fraction does he spend on food and rent together?
B. What fraction of his wages is left to spend on other things?
C. If in a month the same man spend $450 on food, what is his monthly wage?
C. why switch to decimals?
1/3 x = 450
To answer these questions, we need to understand fractions and how to calculate them.
A. To find the fraction the man spends on food and rent together, we need to add the fractions for food and rent. Since the man spends one-third of his wages on food and one-fifth on rent, the total fraction spent on food and rent can be found by adding 1/3 and 1/5.
Step 1: Find a common denominator.
To add fractions, we need a common denominator. In this case, the common denominator for 3 and 5 is 15 (the least common multiple of 3 and 5).
Step 2: Convert fractions with the same denominator.
To convert 1/3 and 1/5 to fractions with a denominator of 15, we can multiply the numerator and denominator of each fraction by the missing factors.
1/3 = (1 x 5) / (3 x 5) = 5/15
1/5 = (1 x 3) / (5 x 3) = 3/15
Step 3: Add the fractions.
Now that both fractions have the same denominator, we can add them:
5/15 + 3/15 = 8/15
Therefore, the man spends 8/15 of his wages on food and rent together.
B. To determine what fraction of his wages is left to spend on other things, we need to subtract the fraction spent on food and rent (8/15) from the whole (1). This can be calculated as:
1 - 8/15 = 15/15 - 8/15 = 7/15
Therefore, the man has 7/15 of his wages left to spend on other things.
C. To calculate the man's monthly wage when he spends $450 on food, we can set up a proportion using the information we have.
Let's denote the monthly wage as "x." If the man spends 1/3 of his wages on food that amounts to $450, we can set up the following equation:
(1/3) * x = $450
To solve for x, we need to isolate it. We can do this by multiplying both sides of the equation by the reciprocal of 1/3, which is 3/1 (or simply 3).
3/1 * (1/3) * x = 3/1 * $450
The fractions cancel out on the left side, leaving:
x = 3 * $450 = $1350
Therefore, the man's monthly wage is $1350.
1/3 + 1/5 = 5/15 + 3/15 = 8/15 spent on food and rent
B -- I think you can figure this out.
C. 0.3333x = 450