Answer:
math using some steps and strategies. Here are the solutions to your questions:
Explanation:
- Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Tshs 100,000, how much money did Anima have?
To solve this problem, we can use the following steps:
1. Define a variable. Let x be the total amount of money that Anima had.
2. Write an equation using the variable. According to the problem, Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. This means that the donation was equal to the remaining fraction of her property after subtracting one-half and one-third. The remaining fraction is 1 - (1/2 + 1/3) = 1/6. So, the equation is:
(1/6)x = 100,000
3. Solve the equation. To find x, we need to multiply both sides of the equation by 6. This gives us:
x = 6 * 100,000
x = 600,000
4. Answer the question. The question asks how much money did Anima have. The answer is x, which we found to be 600,000. So, Anima had Tshs 600,000.
- The cost of a pencil is 25 cents more than the cost of a eraser. If the cost of 8 pencils and 10 erasers is $12.80, find the cost of each.
To solve this problem, we can use the following steps:
1. Define variables. Let p be the cost of a pencil and e be the cost of an eraser.
2. Write equations using the variables. According to the problem, the cost of a pencil is 25 cents more than the cost of an eraser. This means that p = e + 0.25. Also, the cost of 8 pencils and 10 erasers is $12.80. This means that 8p + 10e = 12.80. These are the two equations that we need to solve.
3. Solve the equations. To find p and e, we need to use the substitution method. We can substitute p = e + 0.25 into the second equation and get:
8(e + 0.25) + 10e = 12.80
Simplify and solve for e:
18e + 2 = 12.80
18e = 10.80
e = 0.60
Then, we can plug e = 0.60 into the first equation and get:
p = e + 0.25
p = 0.60 + 0.25
p = 0.85
4. Answer the question. The question asks the cost of each pencil and eraser. The answer is p and e, which we found to be 0.85 and 0.60, respectively. So, the cost of a pencil is $0.85 and the cost of an eraser is $0.60.
- Half of the cost of bread is more than one third of the cost of cheese by $5. If the total cost of the bread and cheese is $35, find the cost of the bread.
To solve this problem, we can use the following steps:
1. Define variables. Let b be the cost of the bread and c be the cost of the cheese.
2. Write equations using the variables. According to the problem, half of the cost of bread is more than one third of the cost of cheese by $5. This means that (1/2)b = (1/3)c + 5. Also, the total cost of the bread and cheese is $35. This means that b + c = 35. These are the two equations that we need to solve.
3. Solve the equations. To find b and c, we need to use the elimination method. We can multiply the first equation by 6 and get:
3b = 2c + 30
Then, we can subtract this equation from the second equation and get:
b + c = 35
-(3b - 2c = 30)
-2b + c = 5
Solve for c:
c = 5 + 2b
Then, we can plug c = 5 + 2b into the first equation and get:
b + (5 + 2b) = 35
Simplify and solve for b:
3b + 5 = 35
3b = 30
b = 10
4. Answer the question. The question asks the cost of the bread. The answer is b, which we found to be 10. So, the cost of the bread is $10.