There were 76 more belts than caps at first. After 158 belts and 30 caps were sold,
there were 3 times as many caps as belts left.
How many belts were there in the end?
Let's define variables for the number of belts and caps at first:
Let b be the number of belts at first.
Let c be the number of caps at first.
Step 1: Establish Equations
From the problem statement:
There were 76 more belts than caps at first:
b=c+76
After selling 158 belts and 30 caps, there were 3 times as many caps as belts left:
Belts left: b−158
Caps left: c−30
Given that caps left are three times the belts left:
c−30=3(b−158)
Step 2: Solve for b and c
Substitute b=c+76 into the second equation:
c−30=3((c+76)−158)
c−30=3(c+76−158)
c−30=3(c−82)
c−30=3c−246
−30+246=3c−c
216=2c
c=108
Find b:
b=108+76=184
Step 3: Find the number of belts left
b−158=184−158=26
Final Answer: There were 26 belts left in the end.
The total mass of an empty school bag and 5 similar books was 5.4 kg. The
total mass of the same school bag and 2 similar books was 3 kg.
What was the mass of 1 book?
Let's define variables:
Let B be the mass of one book (kg).
Let S be the mass of the empty school bag (kg).
Step 1: Establish Equations
From the problem statement:
The total mass of the school bag and 5 books was 5.4 kg:
S+5B=5.4
The total mass of the school bag and 2 books was 3 kg:
S+2B=3
Step 2: Subtract the Two Equations
(S+5B)−(S+2B)=5.4−3
S−S+5B−2B=2.4
3B=2.4
B=2.4 ÷ 3 = 0.8
Final Answer: The mass of one book is 0.8 kg.
Ravi had $92 more than Peter. After Ravi gave $100 to Peter, Peter had 5
times as much as Ravi.
How much money did Ravi have at first?
Let's define variables:
Let R be the amount of money Ravi had at first.
Let P be the amount of money Peter had at first.
Step 1: Establish Equations
From the problem statement:
Ravi had $92 more than Peter:
R=P+92
After Ravi gave $100 to Peter:
Ravi’s new amount: R−100
Peter’s new amount: P+100
Given that Peter now has 5 times as much as Ravi:
P+100=5(R−100)
Step 2: Solve for R and P
Substitute R=P+92 into the second equation:
P+100=5((P+92)−100)
P+100=5(P+92−100)
P+100=5(P−8)
P+100=5P−40
100+40=5P−P
140=4P
P=140 ÷ 4=35
P=35
Find R:
R=P+92=35+92=127
Final Answer: Ravi had $127 at first.