Karin spent Ksh (shillings). 380 to buy 10 books and 3 pencils. Her sister Margaret used Ksh 195 to buy 5 books and two pencils.
a. What is the cost of one book and one pencil ?
b. If their sister, Jane, needs to buy six books and two pencils, how much money does she need ?
list what they have told you:
10b + 3p = 380
5b + 2p = 195
Now just find b and p, and then evaluate 6b+2p
To find the cost of one book and one pencil, we can set up a system of equations using the given information.
Let's assume the cost of one book is "b" shillings, and the cost of one pencil is "p" shillings.
From the information given, we can write the following equations:
Equation 1:
10b + 3p = 380
Equation 2:
5b + 2p = 195
To solve this system of equations, we can use the method of substitution.
Step 1: Solve Equation 2 for "p" in terms of "b".
5b + 2p = 195
2p = 195 - 5b
p = (195 - 5b)/2
Step 2: Substitute the value of "p" in Equation 1 with the expression we obtained in Step 1.
10b + 3((195 - 5b)/2) = 380
Simplify the equation:
10b + 585/2 - 15b/2 = 380
Multiply throughout by 2 to eliminate the fraction:
20b + 585 - 15b = 760
5b = 760 - 585
5b = 175
b = 35
Now, we can substitute the value of "b" back into Equation 2 to find the cost of one pencil:
5(35) + 2p = 195
175 + 2p = 195
2p = 195 - 175
2p = 20
p = 10
a. Therefore, the cost of one book is Ksh 35 and the cost of one pencil is Ksh 10.
b. Now that we know the cost of one book and one pencil, we can calculate the cost for Jane to buy six books and two pencils.
The cost of six books = 6 * 35 = 210 shillings
The cost of two pencils = 2 * 10 = 20 shillings
Therefore, Jane needs 210 + 20 = 230 shillings to buy six books and two pencils.
To find the cost of one book and one pencil, we need to divide the total amount spent by Karin and Margaret by the number of books and pencils they bought respectively.
a. Cost of one book and one pencil:
First, let's find the cost of one book:
Karin spent Ksh 380 on 10 books, so the cost of one book for Karin is 380/10 = Ksh 38.
Next, let's find the cost of one pencil:
Karin spent Ksh 380 on 3 pencils, so the cost of one pencil for Karin is 380/3 = Ksh 126.67 (rounded to two decimal places).
Similarly, let's find the cost of one book and one pencil for Margaret:
Margaret spent Ksh 195 on 5 books, so the cost of one book for Margaret is 195/5 = Ksh 39.
Margaret spent Ksh 195 on 2 pencils, so the cost of one pencil for Margaret is 195/2 = Ksh 97.50 (rounded to two decimal places).
To find the average cost for both Karin and Margaret, we add the costs of each item and divide by the number of items:
The average cost of one book is (38 + 39) / 2 = Ksh 38.50 (rounded to two decimal places).
The average cost of one pencil is (126.67 + 97.50) / 2 = Ksh 112.09 (rounded to two decimal places).
Therefore, the cost of one book and one pencil is approximately Ksh 38.50 and Ksh 112.09 respectively.
b. To find out how much money Jane needs to buy six books and two pencils, we multiply the cost of one book by the number of books and the cost of one pencil by the number of pencils, and then sum the results:
Cost of six books = 6 x Ksh 38.50 = Ksh 231
Cost of two pencils = 2 x Ksh 112.09 = Ksh 224.18 (rounded to two decimal places).
Therefore, Jane needs approximately Ksh 231 + Ksh 224.18 = Ksh 455.18 to buy six books and two pencils.