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Standard XII

Mathematics

Forming simultaneous linear equations

b=2.35+0.25x ...

Question

$b = 2.35 + 0.25 x$
$c = 1.75 + 0.40 x$
In the equations above, $b$ and $c$ represent the price per pound, in dollars, of beef and chicken, respectively, $x$ weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?

2.60$

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2.85$

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2.95$

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3.35$

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Solution

The correct option is D 3.35 $S i n c e w e n e e d t o f i n d t h e p r i c e p e r p o u n d o f b e e f, i . e .$ b $, w h i c h w a s e q u a l t o p r i c e p e r p o u n d o f c h i c k e n, i . e .$ c $, w e e q u a t e$ b $a n d$ c$.
We thus get $2.35 + 0.25 x = 1.75 + 0.40 x$
$\Rightarrow 2.35 - 1.75 = 0.40 x - 0.25 x$
$\Rightarrow 0.60 = 0.15 x$
$\Rightarrow x = 4$
$∴ b = 2.35 + 0.25 x = 2.35 + 0.25 \times 4 = $ 3.35$

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b=2.35+0.25x c=1.75+0.40xIn the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?

The correct option is D 3.35Sinceweneedtofindthepriceperpoundofbeef,i.e.b,whichwasequaltopriceperpoundofchicken,i.e.c,weequatebandc$.We thus get 2.35+0.25x=1.75+0.40x⇒2.35−1.75=0.40x−0.25x⇒0.60=0.15x⇒x=4∴b=2.35+0.25x=2.35+0.25×4=$3.35

$b = 2.35 + 0.25 x$
$c = 1.75 + 0.40 x$
In the equations above, $b$ and $c$ represent the price per pound, in dollars, of beef and chicken, respectively, $x$ weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?