Isabelle bought some stationery. 1/3 of them were pencils. 5/8 of the remainder were erasers and the rest were rulers. The cost of the stationery is - a Pencil: $1.20, an eraser: $1 and a ruler: $0.50. She spent a total of 169.50 on all stationery. How much more did she spend on erasers than rulers.

Isabelle spent $52.50 more on Erasers than rulers.

Step-by-step explanation:

Step 1

Find the quantity of each stationery bought in fraction

Let us represent the total fraction of what Isabelle bought as: x

1/3x = quantity of pencils bought

5/8 of the remainder = quantity of erasers bought

The remainder = x - 1/3x = 2/3x

5/8 of 2/3x = 5/8 × 2/3x = 5/12x

Hence, 5/12x = quantity of erasers bought

The rest is rulers

1 - (1/3 + 5/12)

1 - (4 + 5/12)

1 - 9/12

1 - 3/4

= 1/4x

Hence, 1/4 = quantity of rulers bought.

Step 2

We find the number of stationeries that Isabelle bought.

The cost of the stationery is

a Pencil: $1.20

an eraser: $1

a ruler: $0.50.

Total amount spent on stationery = 169.50

We have this equation

1.20 × 1/3x + 1 × 5/12x + 0.50 × 1/4x = 169.50

0.4x + 0.4166666667x + 0.125x =

169.50

0.9416666667x = 169.50

x = 169.50 /0.9416666667

x = 179.99999999

Approximately , the number of stationeries that Isabelle bought = x = 180

Step 3

Find the number and the amount spent on each stationery that Isabelle bought

a) i) Quantity of pencils bought = 1/3 x

x = 180

= 1/3 × 180

= 60 pencils

ii) Amount spent on pencils

If 1 pencil = $1.20

60 pencils =

60 × 1.20 = $72

b) i) Quantity of Erasers bought = 5/12x

x = 180

= 5/12 × 180

= 75 pencils

ii) Amount spent on Eraser

If 1 pencil = $1

75 pencils =

75 × 1 = $75

c) i) Quantity of rulers bought = 1/4 x

x = 180

= 1/4 × 180

= 45 pencils

ii) Amount spent on pencils

If 1 pencil = $0.50

45 pencils =

45 × 0.50 = $22.50

Step 4

We were asked to calculate how much more did she spend on erasers than rulers.

In step 3, the amount spent on Erasers = $75

the amount spent on ruler = $22.5

The difference in the amount spent = $75 - $22.5

= $52.5

Therefore, Isabelle spent $52.50 more on Erasers than rulers.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry