 # Question

Hello, I need help for this question, it would be highly appreciated.

Bob the builder had twice as many screws as nails.

The total mass of the screws and nails was 1054 g.

The mass of the screws was 646 g more than the mass of the nails.

The mass of each screw was 13 g more than the mass of each nail.

A) What was the mass of the nails in grams?

B) How many Nails were there.

Source: PSLE

Source: PSLE

Total mass of screws = Total mass of nails + 646 g

If the total mass of screws and nails is 1054 g,

Total mass of nails + 646 + Total mass of nails = 1054

A) Total mass of nails = (1054 – 646)/2 = 204 g

Total mass of screws = 204 + 646 = 850 g

Now Bob has twice as many screws than nails and mass of each screw is 13 g more than a nail,

Unit              Mass per unit                       Total Mass (unit x Mass per unit)

Nails                                      1u                       a                                         1ua

Screws                                  2u                      a + 13                                 2u(a + 13)

Total mass of nails -> 1ua -> 204

Total mass of screws -> 2u(a+13) -> 850

2ua + 26u -> 850

26u -> 850 – 2 x 204 = 442  (since 1ua = 204)

1u -> 442/26 = 17

B) There were 17 nails

Checking

Mass of 1 nail -> 204/17 = 12 g

Mass of 1 screw -> 12 + 13 = 25 g

Total number of screws = 34

Total mass of screws and nails = 34 x 25 + 17 x 12 = 1054 g

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A> SCREWS : (1054 – 646)÷2 + 646 = 408÷2 + 646 = 204 + 646 = 850

NAILS : 1054 – 850 = 204

B> if 1u for nails, there are 2u for screws.

850-204 x 2 = 442

442÷ 2 ÷ 13 = 221÷ 13 = 17

So there are 17 nails.

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