Question 989983
Let {{{ a }}} = the larger number
Let {{{ b }}} = the smaller number
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given:
(1) {{{ a - b = 16 }}}
(2) {{{ 3a = 7b }}}
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You have 2 equation with 2 unknowns, so
it is solvable
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Add {{{ b }}} to both sides of (1)
(1) {{{ a = b + 16 }}}
Substitute (1) into (2)
(2) {{{ 3*( b + 16 ) = 7b }}}
(2) {{{ 3b + 48 = 7b }}}
Subtract {{{ 3b }}} from both sides
(2) {{{ 4b = 48 }}}
(2) {{{ b = 12 }}}
and
(1) {{{ a = b + 16 }}}
(1) {{{ a = 12 + 16 }}}
(1) {{{ a = 28 }}}
The larger number is 28
The smaller number is 12
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check:
(1) {{{ a - b = 16 }}}
(1) {{{ 28 - 12 = 16 }}}
The difference is 16
and
(2) {{{ 3a = 7b }}}
(2) {{{ 3*28 = 7*12 }}}
(2) {{{ 84 = 84 }}}
OK